PTITeX 3.4, (c) Personal TeX, Inc. 1985-1998 This is TeX 3.14159 (preloaded format=LATEX 0.11.30) 29 JAN 2001 11:05 **&LATEX C:/FPhandbook/Mesofnoncompactness-LaTeX.tex (C:\FPhandbook\Mesofnoncompactness-LaTeX.tex LaTeX2e <1998/12/01> Babel and hyphenation patterns for american, loaded. (C:\PCTeXv4\AMSLTX12\amsart.cls Document Class: amsart 1995/02/23 v1.2b \linespacing=\dimen102 \normalparindent=\dimen103 \normaltopskip=\skip41 (C:\PCTeXv4\AMSLTX12\amsgen.sty File: amsgen.sty 1995/02/01 v1.2a \@emptytoks=\toks14 \ex@=\dimen104 ) (C:\PCTeXv4\AMSLTX12\amsmath.sty Package: amsmath 1995/02/23 v1.2b AMS math features \@mathmargin=\skip42 (C:\PCTeXv4\AMSLTX12\amstext.sty Package: amstext 1995/01/25 v1.2 ) (C:\PCTeXv4\AMSLTX12\amsbsy.sty Package: amsbsy 1995/01/20 v1.2 \pmbraise@=\dimen105 ) (C:\PCTeXv4\AMSLTX12\amsopn.sty Package: amsopn 1995/02/20 v1.2a operator names ) LaTeX Info: Redefining \frac on input line 180. \uproot@=\count79 \leftroot@=\count80 \classnum@=\count81 \DOTSCASE@=\count82 LaTeX Info: Redefining \dots on input line 327. LaTeX Info: Redefining \ldots on input line 410. LaTeX Info: Redefining \cdots on input line 414. \Mathstrutbox@=\box26 \strutbox@=\box27 \big@size=\dimen106 LaTeX Font Info: Redeclaring font encoding OML on input line 492. LaTeX Font Info: Redeclaring font encoding OMS on input line 493. \skewcharcount@=\count83 \familycount@=\count84 \pointcount@=\count85 \accentdimen@=\dimen107 \accentmu@=\count86 \minaw@=\dimen108 \c@MaxMatrixCols=\count87 \dotsspace@=\muskip10 \c@parentequation=\count88 \dspbrk@lvl=\count89 \tag@help=\toks15 \row@=\count90 \column@=\count91 \maxfields@=\count92 \andhelp@=\toks16 \eqnshift@=\dimen109 \alignsep@=\dimen110 \tagshift@=\dimen111 \tagwidth@=\dimen112 \totwidth@=\dimen113 \lineht@=\dimen114 \@envbody=\toks17 \multlinegap=\skip43 \multlinetaggap=\skip44 ) (C:\PCTeXv4\AMSLTX12\amsfonts.sty Package: amsfonts 1995/02/01 v2.2b \symAMSa=\mathgroup4 \symAMSb=\mathgroup5 LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold' (Font) U/euf/m/n --> U/euf/b/n on input line 128. ) \copyins=\insert233 \abstractbox=\box28 \listisep=\skip45 \c@part=\count93 \c@section=\count94 \c@subsection=\count95 \c@subsubsection=\count96 \c@paragraph=\count97 \c@figure=\count98 \c@table=\count99 \abovecaptionskip=\skip46 \belowcaptionskip=\skip47 (C:\PCTeXv4\AMSLTX12\amsthm.sty Package: amsthm 1995/02/01 v1.2a \theorem@style=\toks18 \theorembodyfont=\toks19 \theoremheadfont=\toks20 \theoremnotefont=\toks21 \theoremheadpunct=\toks22 \theorempreskipamount=\skip48 \theorempostskipamount=\skip49 )) (C:\PCTeXv4\AMSLTX12\amssymb.sty Package: amssymb 1995/02/01 v2.2a ) (C:\PCTeXv4\LATEX2E\newlfont.sty Package: newlfont 1998/08/17 v2.2m Standard LaTeX package LaTeX Info: Redefining \em on input line 49. (C:\PCTeXv4\LATEX2E\latexsym.sty Package: latexsym 1998/08/17 v2.2e Standard LaTeX package (lasy symbols) \symlasy=\mathgroup6 LaTeX Font Info: Overwriting symbol font `lasy' in version `bold' (Font) U/lasy/m/n --> U/lasy/b/n on input line 29. )) (C:\PCTeXv4\LATEX2E\inputenc.sty beta test version Package: inputenc 1998/03/05 v0.97 Input encoding file (test version: still lia ble to change) (C:\PCTeXv4\LATEX2E\ansinew.def File: ansinew.def 1998/03/05 v0.97 Input encoding file (test version: still lia ble to change) )) (C:\PCTeXv4\LATEX2E\graphicx.sty Package: graphicx 1997/06/09 v1.0d Enhanced LaTeX Graphics (DPC,SPQR) (C:\PCTeXv4\LATEX2E\keyval.sty Package: keyval 1998/06/05 v1.11 key=value parser (DPC) \KV@toks@=\toks23 ) (C:\PCTeXv4\LATEX2E\graphics.sty Package: graphics 1998/05/27 v1.0h Standard LaTeX Graphics (DPC,SPQR) (C:\PCTeXv4\LATEX2E\trig.sty Package: trig 1994/10/16 v1.08 sin cos tan (DPC) ) (C:\PCTeXv4\LATEX2E\graphics.cfg) Package graphics Info: Driver file: dvips.def on input line 85. (C:\PCTeXv4\LATEX2E\dvips.def File: dvips.def 1998/05/03 v3.0f Driver-dependant file (DPC,SPQR) )) \Gin@req@height=\dimen115 \Gin@req@width=\dimen116 ) \c@theorem=\count100 \@indexfile=\write3 Writing index file Mesofnoncompactness-LaTeX.idx LaTeX Warning: Unused global option(s): [showkey]. No file Mesofnoncompactness-LaTeX.aux. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 99. LaTeX Font Info: ... okay on input line 99. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 99. LaTeX Font Info: ... okay on input line 99. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 99. LaTeX Font Info: ... okay on input line 99. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 99. LaTeX Font Info: ... okay on input line 99. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 99. LaTeX Font Info: ... okay on input line 99. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 99. LaTeX Font Info: ... okay on input line 99. LaTeX Font Info: Try loading font information for U+msa on input line 99. (C:\PCTeXv4\AMSLTX12\umsa.fd File: Umsa.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+msb on input line 99. (C:\PCTeXv4\AMSLTX12\umsb.fd File: Umsb.fd 1995/01/05 v2.2e AMS font definitions ) LaTeX Font Info: Try loading font information for U+lasy on input line 99. (C:\PCTeXv4\LATEX2E\ulasy.fd File: ulasy.fd 1998/08/17 v2.2eLaTeX symbol font definitions ) No file Mesofnoncompactness-LaTeX.toc. \tf@toc=\write4 LaTeX Warning: Citation `sch' on page 1 undefined on input line 140. LaTeX Warning: Citation `dar' on page 1 undefined on input line 147. LaTeX Warning: Citation `kur' on page 1 undefined on input line 152. LaTeX Warning: Citation `brw' on page 1 undefined on input line 163. LaTeX Warning: Citation `goh' on page 1 undefined on input line 163. LaTeX Warning: Citation `kir' on page 1 undefined on input line 164. LaTeX Warning: Citation `adl' on page 1 undefined on input line 172. LaTeX Warning: Citation `aye' on page 1 undefined on input line 172. LaTeX Warning: Citation `kua' on page 1 undefined on input line 172. LaTeX Warning: Citation `pru' on page 1 undefined on input line 172. LaTeX Warning: Citation `sek' on page 1 undefined on input line 173. [1] LaTeX Warning: Citation `hor' on page 2 undefined on input line 252. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.262 ...hat $\alpha (B_{i(n)} ) <{1\over n}$. ? Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [2] LaTeX Warning: Citation `aye' on page 3 undefined on input line 315. LaTeX Warning: Citation `dar' on page 3 undefined on input line 347. LaTeX Warning: Citation `sad' on page 3 undefined on input line 347. [3] Overfull \hbox (4.0172pt too wide) in paragraph at lines 401--404 []\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 B\OT1/cmr/m/n/10 (0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)$ \OT1/cmr/m/it/10 be the unit ball in a Ba-nach space $\OML/ cmm/m/it/10 X$\OT1/cmr/m/it/10 . Then $\OML/cmm/m/it/10 ^^K\OT1/cmr/m/n/10 (\OM L/cmm/m/it/10 B\OT1/cmr/m/n/10 (0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)) = \OML/ cmm/m/it/10 ^^_\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 B\OT1/cmr/m/n/10 (0\OML/cmm/m/ it/10 ; \OT1/cmr/m/n/10 1)) = [] LaTeX Warning: Citation `kra' on page 4 undefined on input line 428. Overfull \hbox (12.27606pt too wide) in paragraph at lines 448--450 []\OT1/cmr/m/it/10 Let $\OML/cmm/m/it/10 S\OT1/cmr/m/n/10 (0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)$ \OT1/cmr/m/it/10 be the unit sphere in a Ba-nach space $\OM L/cmm/m/it/10 X$\OT1/cmr/m/it/10 . Then $\OML/cmm/m/it/10 ^^K\OT1/cmr/m/n/10 (\ OML/cmm/m/it/10 S\OT1/cmr/m/n/10 (0\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 1)) = \OM L/cmm/m/it/10 ^^_\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 S\OT1/cmr/m/n/10 (0\OML/cmm/ m/it/10 ; \OT1/cmr/m/n/10 1)) = [] Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [4] LaTeX Warning: Citation `don' on page 5 undefined on input line 493. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.543 $$\phi (A_{n+1})<\phi_{n+1}+{1\over {n+1}}.$$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.551 ... (A)\leq\phi (A_n)<\phi_n+{1\over n}\leq\phi (A'\cap A_{n-1}... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.551 ...\leq\phi (A'\cap A_{n-1})+{1\over n}=\phi ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.552 (A')+{1\over n}.$$ ? [5] LaTeX Warning: Citation `aye' on page 6 undefined on input line 598. LaTeX Warning: Citation `don' on page 6 undefined on input line 601. LaTeX Warning: Citation `bar' on page 6 undefined on input line 623. LaTeX Warning: Citation `aye' on page 6 undefined on input line 633. LaTeX Warning: Citation `dul' on page 6 undefined on input line 638. LaTeX Warning: Citation `opi' on page 6 undefined on input line 656. Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [6] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.743 ...a 3.7 we have ${{\alpha (A)}\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.746 ... x_n\}$. Then ${{\alpha (A)}\over ? [7] LaTeX Warning: Citation `ist' on page 8 undefined on input line 761. LaTeX Warning: Citation `aye' on page 8 undefined on input line 781. LaTeX Warning: Citation `ari' on page 8 undefined on input line 782. LaTeX Warning: Citation `erz' on page 8 undefined on input line 783. LaTeX Warning: Citation `gob' on page 8 undefined on input line 791. LaTeX Warning: Citation `gob' on page 8 undefined on input line 829. LaTeX Warning: Citation `ban' on page 8 undefined on input line 830. LaTeX Warning: Citation `dol' on page 8 undefined on input line 831. Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [8] [9] LaTeX Warning: Citation `par' on page 10 undefined on input line 972. LaTeX Warning: Citation `jao' on page 10 undefined on input line 980. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1001 ...lon }\right) ^p\right) ^{1\over p} .$$ for $1\leq ? LaTeX Warning: Citation `bre' on page 10 undefined on input line 1005. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1035 ... $ l \geq \varepsilon /2^{1\over p}$. ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1036 ...eq (1-\varepsilon ^p /2)^{1\over p}$ and ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1039 ...lon }\right) ^p\right) ^{1\over p} .$$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1051 ...\Vert_p = (1-\eta ^P /2)^{1\over ? Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [10] LaTeX Warning: Citation `jao' on page 11 undefined on input line 1056. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1060 ...lon }\right) ^p\right) ^{1\over p} .$$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1074 ...lon }\right) ^p\right) ^{1\over p} .$$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1077 ...lon }\right) ^p\right) ^{1\over p}, $$ for $1< p< ? LaTeX Warning: Citation `gob' on page 11 undefined on input line 1085. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1088 1-\left( { \varepsilon \over 2}\right) ^p\right) ^{1\over p} $$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1088 ...ver 2}\right) ^p\right) ^{1\over p} $$ ? LaTeX Warning: Citation `gil' on page 11 undefined on input line 1132. LaTeX Warning: Citation `kik' on page 11 undefined on input line 1133. [11] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1222 ...K_{n+1})\le \delta (K_n)+{1\over n} ? Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [12] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1249 \text{diam}(K_0)-{1\over n}\le \text{diam}(K_{n+1})-{1\over n}... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1249 ...\le \text{diam}(K_{n+1})-{1\over n} \le \delta(K_n)\le \tex... ? LaTeX Warning: Citation `kir' on page 13 undefined on input line 1265. LaTeX Warning: Citation `bes' on page 13 undefined on input line 1270. LaTeX Warning: Citation `lam' on page 13 undefined on input line 1270. LaTeX Warning: Citation `len' on page 13 undefined on input line 1270. LaTeX Warning: Citation `kam' on page 13 undefined on input line 1271. LaTeX Warning: Citation `kat' on page 13 undefined on input line 1271. LaTeX Warning: Citation `dom' on page 13 undefined on input line 1325. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1327 ...im_{n,m;n\ne m}\V x_n-x_m\V\over \lim_n\V x_n\V}\,\right\} ? [13] LaTeX Warning: Citation `als' on page 14 undefined on input line 1348. LaTeX Warning: Citation `len' on page 14 undefined on input line 1349. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1361 ...im_{\varepsilon \to 1^-}}{1\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1362 ...beta,\tau}(\varepsilon)}={1\over 1-\Delta_{X,\beta,\tau}(1^-)} ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1380 ...im_{n,m;n\ne m}\V x_n-x_m\V\over \lim_n\V x_n\V}\ge ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1381 {{\epsilon + 1\over 2}\over 1 - \Delta_{X,\beta,\tau}(\e)} ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1381 {{\epsilon + 1\over 2}\over 1 - \Delta_{X,\beta,\tau}(\e)} ? LaTeX Warning: Citation `len' on page 14 undefined on input line 1392. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1418 h_0=\sup\left\{ t\ge 1:\,{1\over t}+\Delta_{X,\chi,\tau}\left... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1418 ...ta_{X,\chi,\tau}\left ({1^-\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1426 h(t)={1\over t}+\Delta_{X,\chi,\tau}\left ({1^-\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1426 ...ta_{X,\chi,\tau}\left ({1^-\over ? Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [14] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1442 \left\V y_n-{x_k\over l+\e}\right\V=\left\V {x_n\over l+\e}\r... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1442 ... l+\e}\right\V=\left\V {x_n\over l+\e}\right\V= ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1443 {1\over l+\e}\qquad\hbox{for every }n\in\N. ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1449 {1\over l^\prime}< {1\over l+\e}=\left \V{x_k\over l+\e}\right... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1449 {1\over l^\prime}< {1\over l+\e}=\left \V{x_k\over l+\e}\right... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1449 ... {1\over l+\e}=\left \V{x_k\over l+\e}\right\V\le ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1450 1-\Delta_{X,\chi,\tau}\left({1\over l+2\e}\right)=1- \Delta_{X... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1450 ...elta_{X,\chi,\tau}\left ({1\over l^\prime}\right). ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1462 \quad{1\over ? LaTeX Warning: Citation `aye' on page 15 undefined on input line 1468. LaTeX Warning: Citation `aye' on page 15 undefined on input line 1487. LaTeX Warning: Citation `bym' on page 15 undefined on input line 1490. Overfull \hbox (17.34607pt too wide) in paragraph at lines 1526--1528 \OT1/cmr/m/it/10 for a sub-set $\OML/cmm/m/it/10 B$ \OT1/cmr/m/it/10 of $\OML/c mm/m/it/10 X$\OT1/cmr/m/it/10 . When $\OML/cmm/m/it/10 B \OT1/cmr/m/n/10 = [](\ OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 x[]\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 )$ \OT1/ cmr/m/it/10 we will de-note $\OML/cmm/m/it/10 r[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n /10 f\OML/cmm/m/it/10 x[]\OMS/cmsy/m/n/10 g\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 f\OML/cmm/m/it/10 x[]\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 ))$ \ OT1/cmr/m/it/10 and $\OML/cmm/m/it/10 Z[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 f\OM L/cmm/m/it/10 x[]\OMS/cmsy/m/n/10 g\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 (\OMS/c msy/m/n/10 f\OML/cmm/m/it/10 x[]\OMS/cmsy/m/n/10 g\OT1/cmr/m/n/10 ))$ [] [15] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1591 ...up_{z\in K} \V z-x_0\V<{r+d\over 2} for immediate help. ... l.1651 \Vert Tz_n-{1\over 2} x_n\leq \gamma \delta(\e)\Vert $$ we know ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1656 ...(1-\gamma) Tz_n+{\gamma x_n\over 2}-x_n\Vert$$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1658 +{\gamma \Vert x_n\Vert\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1661 $$\Vert z_n -x_n\Vert \leq {1\over 2}+{1-\gamma\over \gamma} \... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1661 ...t \leq {1\over 2}+{1-\gamma\over \gamma} \Vert ? LaTeX Warning: Citation `gar' on page 17 undefined on input line 1671. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1700 Hence $$\left\V {z_n\over 1/2+\eta}\right\V =\left\V {z_n-z\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1700 ...ta}\right\V =\left\V {z_n-z\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1701 1/2+\eta}+{z\over ? [17] LaTeX Warning: Citation `bro' on page 18 undefined on input line 1745. LaTeX Warning: Citation `goe' on page 18 undefined on input line 1768. ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1782 $$|S|=\sup\left\{{\|Sx-Sy\|\over \|x-y\|}: x,y\in C, x\not= y\... ? Overfull \vbox (1.63055pt too high) has occurred while \output is active [] [18] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1892 ...\V T^{n_i}x_m-T^{n_j} x_m\V\over \tau CS(X)} ? [19] ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1907 B_m\le{s(T)\over \tau CS(X)}\limsup_j\V x_m - T^{n_j} x_m\V. ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1920 ...\left\{ {T^{n_j}x_{m-1}-x_m\over B_{m-1}}\right\}_j ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1927 ...\left\V z_j+{x_m-T^{n_i}x_m\over B_{m-1}}\right\V=\liminf_j{\V ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1928 T^{n_j}x_{m-1}-T^{n_i}x_m\V\over B_{m-1}}\ge ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1931 ...}\left({\V T^{n_i}x_m-x_m\V\over B_{m-1}}\right ). ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1936 ...}\left({\V T^{n_i}x_m-x_m\V\over B_{m-1}}\right )\le {1\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1936 ...over B_{m-1}}\right )\le {1\over ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1940 ...limsup_i\V T^{n_i}x_m-x_m\V\over B_{m-1}}\right )\le s(T) ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1948 ...T^{n_i}x_m - T^{n_j}x_{m-1}\over \eta L_i ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1960 {T^{n_i}x_m - x_m\over L_i B_{m-1}(1+\eta)} . $$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1963 ...;j\ne k}\V {z_j}-{z_k}\V={1\over (1+\eta) ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1968 {1\over L_i(1+\eta) B_{m-1}} \tau CS(X) B_{m-1}.$$ ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1969 Since $$s(T)<{1\over 1+\Delta_{X,\beta,\tau}(1^-)}\leq \tau CS... ? ! Package amsmath Error: Foreign command \over; use \frac or \genfrac instead. See the amsmath package documentation for explanation. Type H for immediate help. ... l.1974 {\V T^{n_i}x_m - x_m\V\over {(1+\eta) L_iB_{m-1}}}\le ? x Here is how much of TeX's memory you used: 1893 strings out of 2873 19404 string characters out of 28518 13613 words of memory out of 73728 4576 multiletter control sequences out of 10000 10974 words of font info for 45 fonts, out of 20000 for 255 176 hyphenation exceptions out of 607 34i,8n,31p,300b,328s stack positions out of 200i,40n,60p,5000b,600s Output written on C:\FPhandbook\Mesofnoncompactness-LaTeX.dvi (19 pages, 99488 bytes).