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1、VeryincompletelistoferrataforV.A.Zorich:MathematicalAnalysisI+IIM.M¨ugerJune14,2007Notethatline−5meansline5countingfromthebottomofthepage.1CorrectionstoVolumeI•p.19,Definition1:ArelationRbetweentwosetsXandYisasubsetofX×Y.•p.35,l.-3:Replace‘thesetof’by‘amodelofthe’.•p.50,Definiti
2、on4:Realnumbers....(Anyway,thiswayofdefiningrationalnumbersisjustabsurd.)•p.54.l.11:Replace‘>’by‘≥’.•p.138,firstparagraph:Zorichisbeingvaguehere:‘growsapproximatelylike...’.Chebyshevprovedtwothings:1.therearenumbersC1,C2suchthatxxC1≤π(x)≤C2.lnxlnx2.Iflimx→∞x/lnxexiststhenitmustb
3、eequalto1.==•p.141,Definition24:shouldbe‘fO(g)andgO(f)’.BB•p.169,Exercise4c):Thisclaimiswrong!ForacounterexampleseeW.M.Boyce:Commutingfunctionswithnocommonfixedpoint.Trans.Amer.Math.Soc.137,77-92(1969).•p.283,Theorem2:ItshouldbenotedthatthisproofwasgivenbyC.Fefferman(Amer.Math.Mo
4、nthly74,(1967))whenhewas18.•p.285,l.-8:Replace‘largerthan’by‘largerthanorequal’.•p.363,middleofthepage:(x−t)′maybeconfusing.Whatismeantisthederivativew.r.t.t,thus−1.•p.397,l.-3:Replaceg′·gbyf′·g.2CorrectionstoVolumeII•p.1,Definition1,b):Replace‘d(x2,x2)’by‘d(x2,x1)’.•p.6,Definit
5、ion7isnon-standard.Shouldbe:‘Apointa∈XisalimitpointofthesetE⊂XifeveryneighborhoodO(a)ofacontainsapointofEotherthana.(Thegivendefinitionisnotequivalenttothestandardoneforallmetricspaces.)•p.18,Exercise1b):Ametricspaceiscompactiffitiscompleteandtotallybounded.Thustheexerciseisnotc
6、orrectasstated.•p.20,Exercise1b):Notcorrectasstated!•p.24,Definition5:changeto‘completemetricspace(Y,d)’.Furthermore,itisbettertoreplace‘everywheredense’by‘dense’sincelateron,mostly‘dense’isused.1•p.26,Definition5’:changeto‘Acompletemetricspace...’.•p.49andfollowing:ThenotationL
7、(X,Y)isusedbothforthesetofalllinearmapsfromXtoY(page49)andforthesetofboundedlinearmaps(Prop.2onpage57).Suggestion:UseL(X,Y)forthelinearandB(X,Y)fortheboundedlinearmaps.•p.73,firstlineofSubsection10.4.1:Replace‘several’by‘one’.•p.75:ThestatementoftheCorollaryissloppy,sincetherea
8、realsohypothesesonxandh!•p.81,Def.2:Thelimitshouldberestricte
