Foundations of the theory of probability

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UNIVERSITY OF FLORIDA LIBRARIES COLLEGE LIBRARY ...

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FOUNDATIONS OF THE THEORY OF PROBABILITY BY A. N. KOLMOGOROV TRANSLATIONEDITEDBY NATHANMORRISON CHELSEA PUBLISHING COMPANY NEW Y ...

SV^A COPYRIGHT 1950 BY CHELSEA PUBLISHINGCOMPANY PRINTEDINU.S.A. ...

« EDITOR'S NOTE In thepreparationof thisEnglishtranslation of Professor Kolmogorov'sfundamentalwork,theoriginalGermanmonograph G ...

Digitized by the Internet Archive in 2013 http://archive.org/details/foundationsoftheOOkolm ...

PREFACE The purpose of this monograph is to give an axiomatic foundationforthetheoryofprobability.Theauthorsethimself thetask of ...

vi Preface Thesixthchaptercontains a survey,withoutproofs,ofsome results ofA.Khinchineandtheauthorofthelimitationsonthe applicab ...

CONTENTS Page EditorsNote. iii Preface — v I. ElementaryTheoryofProbability § Axioms 2 § Therelation toexperimental data 3 § ...

viii Contents V. ConditionalProbabilitiesandMathematical Expectations § Conditionalprobabilities 47 § ExplanationofaBorelpara ...

ChapterI ELEMENTARY THEORY OF PROBABILITY Wedefine as elementary theory ofprobability that partof thetheoryinwhichwehavetodeal w ...

2 I. ElementaryTheory of Probability the system of axioms and in the further development of the theory,then thepostulationalconc ...

§ 2.TheRelationtoExperimental Data 3 Oursystem ofaxiomsisnot,however,complete,forin various problems in the theory of probabilit ...

4 I. ElementaryTheoryofProbability uponrealizationofconditions 8 belongstothesetA (definedin anyway),thenwesaythattheeventAhasta ...

§ NotesonTerminology 5 Remark 1. Iftwo separate statementsare eachpractically reliable,thenwemaysaythatsimultaneouslytheyarebo ...

I. ElementaryTheoryof Probability Theory of Sets The complementary set A = 0. A = E. Thesystem 51 ofthesets A lt A 2 , . ...

§ ImmediateCorollariesoftheAxioms 7 P(AB)=P(A)P A (B). (6) And by inductionweobtain thegeneralformula (the Multi- plication Th ...

8 I. ElementaryTheoryofProbability A lt A 2 , ... , A n areoften called "hypotheses"andformula (14) is consideredas the probabil ...