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Measure theory and probability

Autore: Malcolm Ritchie Adams; Victor Guillemin
Editore: Boston : Birkhäuse, ©1996.
Edizione/Formato:   Libro : EnglishVedi tutte le edizioni e i formati
Banca dati:WorldCat
Sommario:
"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  Per saperne di più…
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Tipo documento: Book
Tutti gli autori / Collaboratori: Malcolm Ritchie Adams; Victor Guillemin
ISBN: 0817638849 9780817638849 3764338849 9783764338848
Numero OCLC: 33668134
Descrizione: xiv, 205 p. : ill. ; 24 cm.
Contenuti: Measure theory --
Integration --
Fourier analysis.
Responsabilità: Malcolm Adams, Victor Guillemin.
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Abstract:

Suitable for instructors and students of statistical measure theoretic courses, this title features numerous informative exercises, and helpful hints or solution outlines with many of the problems.  Per saperne di più…

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"...the text is user friendly to the topics it considers and should be very accessible...Instructors and students of statistical measure theoretic courses will appreciate the numerous informative Per saperne di più…

 
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schema:reviewBody""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."--BOOK JACKET."
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