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Description - Measures, Integrals and Martingales by Rene L. Schilling

This is a concise and elementary introduction to measure and integration theory as it is nowadays needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, differentiation of measures, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis in R are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions will be available on the internet.

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Book Details

ISBN: 9780521615259
ISBN-10: 0521615259
Format: Paperback
(247mm x 174mm x 24mm)
Pages: 396
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 10-Nov-2005
Country of Publication: United Kingdom

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Author Biography - Rene L. Schilling

Rene Schilling is a Professor of Stochastics at the University of Marburg.