Measures, integrals and martingales:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Ausgabe: | Repr. with corr. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 383 S. graph. Darst. |
| ISBN: | 9780521850155 9780521615259 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804150282821566464 |
|---|---|
| adam_text | Titel: Measures, integrals and martingales
Autor: Schilling, René L
Jahr: 2011
Contents
Prelude page viii
Dependence chart xi
1 Prologue 1
Problems 4
2 The pleasures of counting 5
Problems 13
3 tr-algebras 15
Problems 20
4 Measures 22
Problems 28
5 Uniqueness of measures 31
Problems 36
6 Existence of measures 37
Problems 47
7 Measurable mappings 50
Problems 55
8 Measurable functions 58
Problems 66
9 Integration of positive functions 68
Problems 74
10 Integrals of measurable functions and null sets 77
Null sets and the a.e. 81
Problems 85
V
vi Contents
11 Convergence theorems and their applications 89
Parameter-dependent integrals 92
Riemann vs. Lebesgue integration 93
Examples 99
Problems 101
12 The function spaces £?, 1 ^ oo 106
Problems 117
13 Product measures and Fubini s theorem 121
More on measurable functions 128
Distribution functions 129
Minkowski s inequality for integrals 131
Problems 131
14 Integrals with respect to image measures 135
Convolutions 138
Problems 141
15 Integrals of images and Jacobi s transformation rule 143
Jacobi s transformation formula 148
Spherical coordinates and the volume of the unit ball 153
Continuous functions are dense in Lp(A ) 157
Regular measures 159
Problems 160
16 Uniform integrability and Vitali s convergence theorem 164
Different forms of uniform integrability 169
Problems 174
17 Martingales 177
Problems 189
18 Martingale convergence theorems 191
Problems 201
19 The Radon-Nikodym theorem and other applications
of martingales 203
The Radon-Nikodym theorem 203
Martingale inequalities 212
The Hardy-Littlewood maximal theorem 214
Lebesgue s differentiation theorem 219
The Calderón-Zygmund lemma 222
Problems 223
Contents vii
20 Inner product spaces 227
Problems 233
21 Hilbert space Q 235
Problems 247
22 Conditional expectations in L2 249
On the structure of subspaces of L2 254
Problems 258
23 Conditional expectations in LP 259
Classical conditional expectations 264
Separability criteria for the spaces LP(X, A, (jl) 270
Problems 275
24 Orthonormal systems and their convergence behaviour 277
Orthogonal polynomials 277
The trigonometric system and Fourier series 284
The Haar system 290
The Haar wavelet 296
The Rademacher functions 300
Well-behaved orthonormal systems 303
Problems 313
Appendix A: lim inf and lim sup 315
Appendix B: Some facts from point-set topology 320
Topological spaces 321
Metric spaces 324
Normed spaces 327
Appendix C: The volume of a parallelepiped 330
Appendix D: Non-measurable sets 332
Appendix E: A summary of the Riemann integral 339
The (proper) Riemann integral 339
The fundamental theorem of integral calculus 348
Integrals and limits 353
Improper Riemann integrals 355
Further reading 362
References 366
Notation index 369
Name and subject index 373
|
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Schilling, René L. 1969- Verfasser (DE-588)122050045 aut Measures, integrals and martingales René L. Schilling Repr. with corr. Cambridge [u.a.] Cambridge Univ. Press 2011 X, 383 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Integrals Martingales (Mathematics) Measure theory Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s 1\p DE-604 DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025947292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schilling, René L. 1969- Measures, integrals and martingales Integrals Martingales (Mathematics) Measure theory Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4138369-2 (DE-588)4074626-4 (DE-588)4151278-9 |
| title | Measures, integrals and martingales |
| title_auth | Measures, integrals and martingales |
| title_exact_search | Measures, integrals and martingales |
| title_full | Measures, integrals and martingales René L. Schilling |
| title_fullStr | Measures, integrals and martingales René L. Schilling |
| title_full_unstemmed | Measures, integrals and martingales René L. Schilling |
| title_short | Measures, integrals and martingales |
| title_sort | measures integrals and martingales |
| topic | Integrals Martingales (Mathematics) Measure theory Integrationstheorie (DE-588)4138369-2 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Integrals Martingales (Mathematics) Measure theory Integrationstheorie Maßtheorie Einführung |
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