Measures, Integrals and Martingales

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Cambridge University Press, 10.11.2005
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This book, first published in 2005, introduces measure and integration theory as it is 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, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis 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 can be found on the author's website, which can be reached from www.cambridge.org/9780521615259.
 

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Inhalt

7
49
8
57
9
67
10
76
11
88
12
105
13
120
14
134
16
163
17
176
18
190
19
202
20
226
21
234
22
248
23
258

15
142
24
276

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Über den Autor (2005)

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

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