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1、MarekCapinskiandEkkehardKoppMeasure,IntegralandProbabilitySpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestToourchildren;grandchildren:Piotr,Maciej,Jan,Anna;LukaszAnna,EmilyPrefaceThecentralconceptsinthisbookareLebesguemeasureandtheLebes
2、gueintegral.TheirroleasstandardfareinUKundergraduatemathematicscoursesisnotwhollysecure;yettheyprovidetheprincipalmodelforthedevelopmentoftheabstractmeasurespaceswhichunderpinmodernprobabilitytheory,whiletheLebesguefunctionspacesremainthemainsourceofexamplesonwhichtot
3、estthemethodsoffunctionalanalysisanditsmanyapplications,suchasFourieranalysisandthetheoryofpartialdi erentialequations.Itfollowsthatnotonlybuddinganalystshaveneedofaclearunderstandingoftheconstructionandpropertiesofmeasuresandintegrals,butalsothatthosewhowishtocontrib
4、uteseriouslytotheapplicationsofanalyticalmethodsinawidevarietyofareasofmathematics,physics,electronics,engineeringand,mostrecently, nance,needtostudytheunderlyingtheorywithsomecare.Wehavefoundremarkablyfewtextsinthecurrentliteraturewhichaimexplicitlytoprovideforthesen
5、eeds,atalevelaccessibletocurrentunder-graduates.Therearemanygoodbooksonmodernprobabilitytheory,andincreasinglytheyrecognizetheneedforastronggroundinginthetoolswedevelopinthisbook,butalltoooftenthetreatmentiseithertooadvancedforanundergraduateaudienceorelsesomewhatperf
6、unctory.Wehopethereforethatthecurrenttextwillnotberegardedasonewhich llsamuch-neededgapintheliterature!Onefundamentaldecisionindevelopingatreatmentofintegrationiswhethertobeginwithmeasuresorintegrals,i.e.whethertostartwithsetsorwithfunctions.Functionalanalystshavetend
7、edtofavourthelatterapproach,whiletheformerisclearlynecessaryforthedevelopmentofprobability.Wehavedecidedtosidewiththeprobabilistsinthisargument,andtousethe(reasonably)systematicdevelopmentofbasicconceptsandresultsinproba-bilitytheoryastheprincipal eldofapplication{the
8、orderoftopicsandtheviiviiiPrefaceterminologyweusere
ectthischoice,andeachchapterconcludeswithfurtherdevelopmentoftherelevant
