PTITeX 3.4, (c) Personal TeX, Inc. 1985-1998 This is TeX 3.14159 (preloaded format=LATEX 0.11.30) 20 MAR 2001 10:06 **&LATEX C:/FPhandbook/hb-classical.tex (C:\FPhandbook\hb-classical.tex LaTeX2e <1998/12/01> Babel and hyphenation patterns for american, loaded. 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(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:\PCTeXv4\AMSLTX12\amscd.sty Package: amscd 1995/02/01 v1.2a \athelp@=\toks24 \bigaw@=\dimen117 \minCDarrowwidth=\dimen118 ) (C:\PCTeXv4\AMSLTX12\amssymb.sty Package: amssymb 1995/02/01 v2.2a ) \c@acknowledgement=\count100 \c@algorithm=\count101 \c@axiom=\count102 \c@case=\count103 \c@claim=\count104 \c@conclusion=\count105 \c@condition=\count106 \c@conjecture=\count107 \c@corollary=\count108 \c@criterion=\count109 \c@definition=\count110 \c@example=\count111 \c@exercise=\count112 \c@lemma=\count113 \c@notation=\count114 \c@problem=\count115 \c@proposition=\count116 \c@remark=\count117 \c@solution=\count118 \c@summary=\count119 \c@theorem=\count120 (C:/FPhandbook/hb-classical.aux) LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 45. LaTeX Font Info: ... okay on input line 45. 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Overfull \hbox (3.53065pt too wide) in paragraph at lines 846--851 \OT1/cmr/m/it/10 with the nat-ural ex-ten-sion $\OML/cmm/m/it/10 T\OT1/cmr/m/n/ 10 0 = \OML/cmm/m/it/10 e[]$\OT1/cmr/m/it/10 , where $\OML/cmm/m/it/10 e[] \OT1 /cmr/m/n/10 = [] \OML/cmm/m/it/10 ;$ \OT1/cmr/m/it/10 and $\OML/cmm/m/it/10 Px \OT1/cmr/m/n/10 = []$ [] LaTeX Warning: Reference `ar' on page 11 undefined on input line 888. [11] LaTeX Warning: Citation `dominguez' on page 12 undefined on input line 909. LaTeX Warning: Citation `jimenez3' on page 12 undefined on input line 913. LaTeX Warning: Citation `lin3' on page 12 undefined on input line 923. LaTeX Warning: Citation `ayerbe' on page 12 undefined on input line 930. LaTeX Warning: Citation `gulevich' on page 12 undefined on input line 931. [12] LaTeX Warning: Citation `brodskii-milman' on page 13 undefined on input line 98 5. LaTeX Warning: Citation `maurey' on page 13 undefined on input line 988. 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[16] Overfull \hbox (7.80904pt too wide) in paragraph at lines 1311--1315 []\OT1/cmr/m/n/10 Now sup-pose there ex-ists a point $\OML/cmm/m/it/10 z \OMS/c msy/m/n/10 2 \OML/cmm/m/it/10 K$ \OT1/cmr/m/n/10 such that $\OML/cmm/m/it/10 r\ OT1/cmr/m/n/10 (\OML/cmm/m/it/10 z\OT1/cmr/m/n/10 ) [] \OML/cmm/m/it/10 A:$ \OT 1/cmr/m/n/10 Since $[] \OMS/cmsy/m/n/10 ^^T [] [17] Overfull \hbox (4.08812pt too wide) in paragraph at lines 1340--1347 \OT1/cmr/m/n/10 Thus $[\OML/cmm/m/it/10 f \OMS/cmsy/m/n/10 ^^N \OML/cmm/m/it/10 r\OT1/cmr/m/n/10 ] \OMS/cmsy/m/n/10 ^^V \OT1/cmr/m/n/10 [\OML/cmm/m/it/10 r\OT 1/cmr/m/n/10 ]\OML/cmm/m/it/10 :$ \OT1/cmr/m/n/10 But since $[\OML/cmm/m/it/10 r\OT1/cmr/m/n/10 ]$ is min-i-mal this im-plies $[] = [] \OML/cmm/m/it/10 > [] LaTeX Warning: Citation `lim1' on page 18 undefined on input line 1360. [18] LaTeX Warning: Citation `bruck3' on page 19 undefined on input line 1429. LaTeX Warning: Citation `bruck-goebel' on page 19 undefined on input line 1461. 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LaTeX Warning: Citation `aronszajn-panitchpakdi' on page 31 undefined on input line 2371. LaTeX Warning: Citation `van de vel' on page 31 undefined on input line 2387. LaTeX Warning: Citation `van de vel' on page 31 undefined on input line 2390. [31] Overfull \hbox (1.46986pt too wide) in paragraph at lines 2454--2457 \OT1/cmr/m/n/10 Notice that if $\OMS/cmsy/m/n/10 A\OT1/cmr/m/n/10 (\OML/cmm/m/i t/10 X\OT1/cmr/m/n/10 )$ de-notes the fam-ily of all ad-mis-si-ble sub-sets of $\OML/cmm/m/it/10 X;$ \OT1/cmr/m/n/10 then $(\OML/cmm/m/it/10 X; \OMS/cmsy/m/n/ 10 A\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 X\OT1/cmr/m/n/10 ))$ [] [32] LaTeX Warning: Citation `Kelley' on page 33 undefined on input line 2529. [33] LaTeX Warning: Reference `prop-m1' on page 34 undefined on input line 2578. LaTeX Warning: Reference `prob1' on page 34 undefined on input line 2579. LaTeX Warning: Reference `prop-m1' on page 34 undefined on input line 2597. 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Rerun to get cross-references right. ) Here is how much of TeX's memory you used: 2065 strings out of 2873 20940 string characters out of 28518 95101 words of memory out of 81920 4756 multiletter control sequences out of 10000 14606 words of font info for 55 fonts, out of 20000 for 255 176 hyphenation exceptions out of 607 34i,14n,32p,276b,415s stack positions out of 200i,40n,60p,5000b,600s Output written on C:\FPhandbook\hb-classical.dvi (42 pages, 212908 bytes).