Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Measure Theory and Probability

Measure Theory and Probability

Adams, Malcolm, Guillemin, Victor

1996, XVI, 206 p.

A product of Birkhäuser Basel
Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$39.99

(net) price for USA

ISBN 978-1-4612-0779-5

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$59.95

(net) price for USA

ISBN 978-0-8176-3884-9

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

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

Content Level » Research

Keywords » Lebesgue measure - Probability theory - calculus - ksa - measure theory - proof - random walk - theorem

Related subjects » Birkhäuser Applied Probability and Statistics - Birkhäuser Mathematics

Table of contents 

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

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Measure and Integration.

Additional information