Measure Theory and Probability

by Malcolm Adams, Victor Guillemin

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.
--back cover

Genres: Mathematics

228 pages, Hardcover

First published January 1, 1986

Reviews

[Muhammad Kamran]

its my course book and i am very happy that i find it in the goodreads site.

[David]

Basic measure theory, the Lebesgue Integral, and how they relate to Probability and Fourier Analysis.