RT Book, Whole DB /z-wcorg/ DS http://worldcat.org ID 33668134 LA English T1 Measure theory and probability A1 Adams, Malcolm Ritchie., Guillemin, Victor,, PB Birkhäuse PP Boston YR 1996 SN 0817638849 9780817638849 3764338849 9783764338848 AB "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.