Measure Theory and Probability
by Malcolm Adams and Victor Guillemin
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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, 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.
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Measure Theory and Probability
1996, Birkhäuser
Hardcover
in English
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0817638849 9780817638849
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Measure theory and probability
1986, Wadsworth & Brooks/Cole Advanced Books and Software
in English
0534063306 9780534063306
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Includes bibliographical references (p. 202) and index.
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| November 20, 2020 | Edited by MARC Bot | import existing book |
| July 28, 2019 | Edited by Lisa | Edited without comment. |
| July 28, 2019 | Edited by Lisa | Added new cover |
| July 28, 2019 | Edited by Lisa | Update covers |
| December 10, 2009 | Created by WorkBot | add works page |