Measures and probabilities:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a]
Springer
1996
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 510 S. |
| ISBN: | 0387946446 |
Staff View
MARC
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| 100 | 1 | |a Simonnet, Michel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Measures and probabilities |c Michel Simonnet |
| 264 | 1 | |a New York [u.a] |b Springer |c 1996 | |
| 300 | |a XIII, 510 S. | ||
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| 490 | 0 | |a Universitext | |
| 650 | 4 | |a Daniell-Integral | |
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| 650 | 4 | |a Wahrscheinlichkeitstheorie - Lehrbuch | |
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| 650 | 4 | |a Probabilities | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Foreword v
Preface vii
I Integration Relative to Daniell Measures 1
1 Riesz Spaces 3
1.1 Ordered Groups 4
1.2 Riesz Spaces 9
1.3 Order Dual of a Riesz Space 12
1.4 Daniell Measures 16
2 Measures on Semirings 26
2.1 Semirings, Rings, and 7 Rings 26
2.2 Measures on Semirings 30
2.3 Lebesgue Measure on an Interval 38
3 Integrable and Measurable Functions 40
3.1 Upper Integral of a Positive Function 41
3.2 Convergence Theorems 49
3.3 Integrable Sets 56
3.4 (j Measurable Spaces 60
3.5 Measurable Mappings 62
3.6 Essentially Integrable Mappings 66
x Contents
3.7 Upper and Lower Integrals 70
3.8 Atoms 78
3.9 Prolongations of fi 81
4 Lebesgue Measure on R 86
4.1 Base 6 Expansions of a Real Number 86
4.2 The Cantor Singular Function 88
4.3 Example of a Nonmeasurable Set 90
5 V Spaces 93
5.1 Definition of Lp Spaces 94
5.2 Convergence Theorems 99
5.3 Convergence in Measure 104
5.4 Uniformly Integrable Sets 108
6 Integrable Functions for Measures on Semirings 121
6.1 Measurability 121
6.2 Complements on the Lp Spaces 126
6.3 Measures Denned by Masses 127
6.4 Prolongations of a Measure 128
7 Radon Measures 133
7.1 Locally Compact Spaces 134
7.2 Radon Measures 137
7.3 Regularity of Radon Measures 140
7.4 Lusin Measurable Mappings 143
7.5 Atomic Radon Measures 145
7.6 The Riemann Integral 147
7.7 Weak Convergence 153
7.8 Tight Sequences 157
8 Regularity 166
8.1 Regular Measures 166
II Operations on Measures Defined on Semirings 173
9 Induced Measures and Product Measures 175
9.1 Measure Induced on a Measurable Set 175
9.2 Fubini s Theorem 178
9.3 Lebesgue Measure on R* 187
10 Radon Nikodym Derivatives 193
10.1 Sums of Measures 194
10.2 Locally Integrable Functions 195
10.3 The Radon Nikodym Theorem 200
Contents xi
10.4 Combination of Operations on Measures 205
10.5 Duality of L Spaces 207
10.6 The Yosida Hewitt Decomposition Theorem 210
11 Images of Measures 224
11.1 /x Suited Pairs 225
11.2 Infinite Product of Measures 228
11.3 Change of Variable 233
11.4 Elements of Ergodic Theory 236
12 Change of Variables 242
12.1 Differentiation in Rk 242
12.2 The Modulus of an Automorphism 248
12.3 Change of Variables 250
12.4 Polar Coordinates 252
13 Stieltjes Integral 265
13.1 Functions of Bounded Variation 266
13.2 Stieltjes Measures 268
13.3 Line Integrals 274
13.4 The Lebesgue Decomposition of a Function 277
13.5 Upper and Lower Derivatives 282
14 The Fourier Transform in Rfc 286
14.1 Measures in Rfc 287
14.2 Distribution Functions 293
14.3 Covariance Matrix 294
14.4 The Fourier Transform 296
14.5 Normal Laws in R 303
III Convergence of Random Variables; Conditional
Expectation 309
15 The Strong Law of Large Numbers 311
15.1 Convergence in Probability 312
15.2 Independence of Random Variables 313
15.3 An Example of Independent Random Variables 316
15.4 The One Sided Shift Transformation 318
15.5 Borel s Normal Number Theorem 320
16 The Central Limit Theorem 326
16.1 Convergence in Law 326
16.2 The Lindeberg Theorem 330
16.3 The Central Limit Theorem 334
xii Contents
17 Order Statistics 344
17.1 Definition of the Order Statistics 344
17.2 Convergence of the Empirical Median 347
18 Conditional Probability 352
18.1 Conditional Expectation 353
18.2 The Converse of the Mean Value Theorem 358
18.3 Jensen s Inequality 360
18.4 Conditional Expected Value Given a Random Variable . . 363
18.5 Conditional Law of Y Given X 364
18.6 Computation of Conditional Laws 369
18.7 Existence of Conditional Laws when G = Rk 371
IV Operations on Radon Measures 377
19 [i Adequate Family of Measures 379
19.1 Induced Radon Measure 380
19.2 /x Dense Families of Compact Sets 382
19.3 Sums of Radon Measures 385
19.4 /^ Adequate Families 387
19.5 ^ Adapted Pairs 391
20 Radon Measures Defined by Densities 397
20.1 Integration with Respect to Induced Measures 397
20.2 Radon Measures with Base fx 399
20.3 The Radon Nikodym Theorem 402
20.4 Duality of Lp Spaces 405
21 Images of Radon Measures and Product Measures 408
21.1 Images of Radon Measures 408
21.2 Decomposition of a Measure in Slices 410
21.3 Product of Radon Measures 411
22 Operations on Regular Measures 416
22.1 Some Operations on Regular Measures 416
22.2 Baire Sets 419
22.3 Product of Regular Measures 421
22.4 Change of Variable Formula 423
23 Haar Measures 425
23.1 Invariant Measures 426
23.2 Existence and Uniqueness of Left Haar Measure 429
23.3 Modular Function on G 433
23.4 Relatively Invariant Measures on a Group 434
23.5 Homogeneous Spaces 436
Contents xiii
23.6 Integration with Respect to A8 442
23.7 Reconstitution of AL 444
23.8 Quasi Invariant Measures on Homogeneous Spaces .... 446
23.9 Relatively Invariant Measures on G/H 449
23.10 Haar Measure on 50(n + l,R) 450
23.11 Haar Measure on SH(n,R) 454
24 Convolution of Measures 465
24.1 Convolvable Measures 466
24.2 Convolution of a Measure and a Function 467
24.3 Convolution of a Measure and a Continuous Function . . 471
24.4 Convolution of/z € M(G,C) and / € / (/?) 472
24.5 Convolution and Transposition 476
24.6 Convolution of Functions on a Group 479
24.7 Regularization 483
24.8 Definition of Gelfand Pair 488
Index 499
Symbol Index 505
|
| any_adam_object | 1 |
| author | Simonnet, Michel |
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| dewey-search | 515/.783 20 |
| dewey-sort | 3515 3783 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:01:19Z |
| institution | BVB |
| isbn | 0387946446 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007313279 |
| oclc_num | 246893082 |
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| physical | XIII, 510 S. |
| publishDate | 1996 |
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| publisher | Springer |
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| series2 | Universitext |
| spelling | Simonnet, Michel Verfasser aut Measures and probabilities Michel Simonnet New York [u.a] Springer 1996 XIII, 510 S. txt rdacontent n rdamedia nc rdacarrier Universitext Daniell-Integral Lehrbuch - Integrationstheorie Maßtheorie - Lehrbuch Wahrscheinlichkeitstheorie - Lehrbuch Measure theory Probabilities Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007313279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simonnet, Michel Measures and probabilities Daniell-Integral Lehrbuch - Integrationstheorie Maßtheorie - Lehrbuch Wahrscheinlichkeitstheorie - Lehrbuch Measure theory Probabilities Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074626-4 |
| title | Measures and probabilities |
| title_auth | Measures and probabilities |
| title_exact_search | Measures and probabilities |
| title_full | Measures and probabilities Michel Simonnet |
| title_fullStr | Measures and probabilities Michel Simonnet |
| title_full_unstemmed | Measures and probabilities Michel Simonnet |
| title_short | Measures and probabilities |
| title_sort | measures and probabilities |
| topic | Daniell-Integral Lehrbuch - Integrationstheorie Maßtheorie - Lehrbuch Wahrscheinlichkeitstheorie - Lehrbuch Measure theory Probabilities Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Daniell-Integral Lehrbuch - Integrationstheorie Maßtheorie - Lehrbuch Wahrscheinlichkeitstheorie - Lehrbuch Measure theory Probabilities Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007313279&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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