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Measure Theory and Probability de Malcolm Adams

Measure Theory and Probability: The Wadsworth & Brooks/Cole Mathematics Series

Autor Malcolm Adams, Victor Guillemin
en Limba Engleză Hardback – 26 ian 1996
"…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 exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association
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Specificații

ISBN-13: 9780817638849
ISBN-10: 0817638849
Pagini: 206
Ilustrații: XVI, 206 p.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.48 kg
Ediția:1996
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria The Wadsworth & Brooks/Cole Mathematics Series

Locul publicării:Boston, MA, United States

Public țintă

Research

Cuprins

1 Measure Theory.- 2 Integration.- 3 Fourier Analysis.- Appendix A Metric Spaces.- Appendix C A Non-Measurable Subset of the Interval (0, 1].- References.

Recenzii

"…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 exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association

Textul de pe ultima copertă

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 Szegö theorem and the central limit theorem. In this concise text, quite a few applications to probability are packed into the exercises.
"…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 exercises; helpful hints or solution outlines are given with many of the problems. All in all, the text should make a useful reference for professionals and students."—The Journal of the American Statistical Association