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- catalog abstract ""Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. The measure-theoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on R [superscript n] (metric space approach), the Borel-Cantelli lemmas, straight measure theory (the Lebesgue integral). Chapter 3 expands on abstract Fourier analysis, Fourier series and the Fourier integral, which have some beautiful probabilistic applications: Polya's theorem on random walks, Kac's proof of the Szego theorem and the central limit theorem. In this concise text, quite a few applications to probability are packed into the exercises."--Jacket.".
- catalog contributor b9222218.
- catalog contributor b9222219.
- catalog contributor b9222220.
- catalog created "c1996.".
- catalog date "1996".
- catalog date "c1996.".
- catalog dateCopyrighted "c1996.".
- catalog description ""Measure theory and integration are presented to undergraduates from the perspective of probability theory. The first chapter shows why measure theory is needed for the formulation of problems in probability, and explains why one would have been forced to invent Lebesgue theory (had it not already existed) to contend with the paradoxes of large numbers. The measure-theoretic approach then leads to interesting applications and a range of topics that include the construction of the Lebesgue measure on R [superscript n] (metric space approach), the Borel-Cantelli lemmas, straight measure theory (the Lebesgue integral). Chapter 3 expands on abstract Fourier analysis, Fourier series and the Fourier integral, which have some beautiful probabilistic applications: Polya's theorem on random walks, Kac's proof of the Szego theorem and the central limit theorem. In this concise text, quite a few applications to probability are packed into the exercises."--Jacket.".
- catalog description "Includes bibliographical references (p. 202) and index.".
- catalog description "Measure theory -- Integration -- Fourier analysis.".
- catalog extent "xiv, 205 p. :".
- catalog identifier "0817638849 (hc : alk. paper)".
- catalog identifier "3764338849 (Basel : hc : alk. paper)".
- catalog issued "1996".
- catalog issued "c1996.".
- catalog language "eng".
- catalog publisher "Boston : Birkhäuse,".
- catalog subject "515/.42 20".
- catalog subject "Measure theory.".
- catalog subject "Probabilities.".
- catalog subject "QA273 .A414 1995".
- catalog tableOfContents "Measure theory -- Integration -- Fourier analysis.".
- catalog title "Measure theory and probability / Malcolm Adams, Victor Guillemin.".
- catalog type "text".