Measures, Integrals and Martingales

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Cambridge University Press, 03.04.2017 - 490 Seiten
0 Rezensionen
A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon-Nikodym theorem, differentiation of measures and Hardy-Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon-Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author's webpage at www.motapa.de.
 

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Inhalt

c01
1
C02
6
c03
16
C04
23
c05
32
C06
39
C07
53
c08
60
c21
238
C22
258
C23
275
c24
288
C25
300
c26
322
c27
341
C28
370

C09
72
C10
82
c11
89
C12
96
c13
116
C14
136
c15
154
C16
164
c17
186
c18
197
c19
214
C20
230
APPA
409
AppB
415
Appc
421
APPD
423
APPE
425
AppF
427
Appg
429
Apph
437
Appi
441
REF
465
Index
469
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Über den Autor (2017)

René L. Schilling is a Professor of Mathematics at Technische Universität, Dresden. His main research area is stochastic analysis and stochastic processes.

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