Measure theory: 2
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
[2007]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiii, 575 Seiten |
| ISBN: | 9783540345138 |
Internformat
MARC
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| 100 | 1 | |a Bogačev, Vladimir I. |d 1961- |e Verfasser |0 (DE-588)121192318 |4 aut | |
| 245 | 1 | 0 | |a Measure theory |n 2 |c V. I. Bogachev |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c [2007] | |
| 300 | |a xiii, 575 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-015606326 | ||
Datensatz im Suchindex
| _version_ | 1804136458088349696 |
|---|---|
| adam_text | Contents
Preface
to Volume
2...................................................
v
Chapter
6.
Borei,
Baire and Souslin sets
...........................1
6.1.
Metric and topological spaces
.................................1
6.2.
Borei
sets
....................................................10
6.3.
Baire sets
....................................................12
6.4.
Products of topological spaces
................................14
6.5.
Countably generated
σ
-algebras
..............................
16
6.6.
Souslin sets and their separation
.............................19
6.7.
Sets in Souslin spaces
........................................24
6.8.
Mappings of Souslin spaces
...................................28
6.9.
Measurable choice theorems
..................................33
6.10.
Supplements and exercises
...................................43
Borei
and Baire sets
(43).
Souslin sets as projections
(46).
/C-analytic
and ^- -analytic sets
(49). Blackwell
spaces
(50).
Mappings of Souslin
spaces
(51).
Measurability in normed spaces
(52).
The Skorohod
space
(53).
Exercises
(54).
Chapter
7.
Measures on topological spaces
.......................67
7.1.
Borei,
Baire and Radon measures
............................67
7.2.
r-additive measures
..........................................73
7.3.
Extensions of measures
.......................................78
7.4.
Measures on Souslin spaces
...................................85
7.5.
Perfect measures
.............................................86
7.6.
Products of measures
........................................92
7.7.
The Kolmogorov theorem
....................................95
7.8.
The
Danieli
integral
..........................................99
7.9.
Measures as functionals
.....................................108
7.10.
The regularity of measures in terms of functionals
...........
Ill
7.11.
Measures on locally compact spaces
.........................113
7.12.
Measures on linear spaces
...................................117
7.13.
Characteristic functionals
...................................120
7.14.
Supplements and exercises
..................................126
Extensions of product measures
(126).
Measurability on products
(129).
Mařík
spaces
(130).
Separable measures
(132).
Diffused and
atomless
measures
(133).
Completion regular measures
(133).
Radon
spaces
(135).
Supports of measures
(136).
Generalizations of Lusin s
theorem
(137).
Metric outer measures
(140).
Capacities
(142).
Covariance operators and means of measures
(142).
The Choquet
representation
(145).
Convolution
(146).
Measurable linear
functions
(149).
Convex measures
(149).
Pointwise convergence
(151).
Infinite Radon measures
(154).
Exercises
(155).
Chapter
8.
Weak convergence of measure
.......................175
8.1.
The definition of weak convergence
..........................175
8.2.
Weak convergence of
nonnegative
measures
..................182
8.3.
The case of metric space
....................................191
8.4.
Some properties of weak convergence
........................194
8.5.
The Skorohod representation
................................199
8.6.
Weak compactness and the Prohorov theorem
...............202
8.7.
Weak sequential completeness
...............................209
8.8.
Weak convergence and the Fourier transform
................210
8.9.
Spaces of measures with the weak topology
..................211
8.10.
Supplements and exercises
..................................217
Weak compactness
(217).
Prohorov spaces
(219).
The Weak sequential
completeness of spaces of measures
(226).
The
Л
-topology
(226).
Continuous mappings of spaces of measures
(227).
separability
of spaces of measures
(230).
Young measures
(231).
Metrics on
spaces of measures
(232).
Uniformly distributed sequences
(237).
Setwise convergence of measures
(241).
Stable convergence and
ws-topology
(246).
Exercises
(249)
Chapter
9.
Transformations of measures and isomorphisms
... 267
9.1.
Images and preimages of measures
..........................267
9.2.
Isomorphisms of measure spaces
.............................275
9.3.
Isomorphisms of measure algebras
...........................277
9.4.
Lebesgue Rohlin spaces
.....................................280
9.5.
Induced point isomorphisms
.................................284
9.6.
Topologically equivalent measures
...........................286
9.7.
Continuous images of Lebesgue measure
.....................288
9.8.
Connections with extensions of measures
....................291
9.9.
Absolute continuity of the images of measures
...............292
9.10.
Shifts of measures along integral curves
.....................297
9.11.
Invariant measures and
Haar
measures
......................303
9.12.
Supplements and exercises
..................................308
Projective
systems of measures
(308).
Extremal preimages of
measures and uniqueness
(310).
Existence of
atomless
measures
(317).
Invariant and quasi-invariant measures of transformations
(318).
Point
and Boolean isomorphisms
(320).
Almost homeomorphisms
(323).
Measures with given marginal projections
(324).
The Stone
representation
(325).
The Lyapunov theorem
(326).
Exercises
(329)
Chapter
10.
Conditional measures and conditional
expectations
..........................................339
10.1.
Conditional expectations
...................................339
10.2.
Convergence of conditional expectations
....................346
10.3.
Martingales
................................................348
10.4.
Regular conditional measures
..............................356
10.5.
Liftings and conditional measures
..........................371
10.6.
Disintegrations of measures
................................380
10.7.
Transition measures
........................................384
10.8.
Measurable partitions
......................................389
10.9.
Ergodic theorems
..........................................391
10.10.
Supplements and exercises
.................................398
Independence
(398).
Disintegrations
(403).
Strong liftings
(406).
Zero-one laws
(407).
Laws of large numbers
(410).
Gibbs
measures
(416).
Triangular mappings
(417).
Exercises
(427).
Bibliographical and Historical Comments
.........................439
References
............................................................465
Author Index
........................................................547
Subject Index
........................................................561
|
| adam_txt |
Contents
Preface
to Volume
2.
v
Chapter
6.
Borei,
Baire and Souslin sets
.1
6.1.
Metric and topological spaces
.1
6.2.
Borei
sets
.10
6.3.
Baire sets
.12
6.4.
Products of topological spaces
.14
6.5.
Countably generated
σ
-algebras
.
16
6.6.
Souslin sets and their separation
.19
6.7.
Sets in Souslin spaces
.24
6.8.
Mappings of Souslin spaces
.28
6.9.
Measurable choice theorems
.33
6.10.
Supplements and exercises
.43
Borei
and Baire sets
(43).
Souslin sets as projections
(46).
/C-analytic
and ^-"-analytic sets
(49). Blackwell
spaces
(50).
Mappings of Souslin
spaces
(51).
Measurability in normed spaces
(52).
The Skorohod
space
(53).
Exercises
(54).
Chapter
7.
Measures on topological spaces
.67
7.1.
Borei,
Baire and Radon measures
.67
7.2.
r-additive measures
.73
7.3.
Extensions of measures
.78
7.4.
Measures on Souslin spaces
.85
7.5.
Perfect measures
.86
7.6.
Products of measures
.92
7.7.
The Kolmogorov theorem
.95
7.8.
The
Danieli
integral
.99
7.9.
Measures as functionals
.108
7.10.
The regularity of measures in terms of functionals
.
Ill
7.11.
Measures on locally compact spaces
.113
7.12.
Measures on linear spaces
.117
7.13.
Characteristic functionals
.120
7.14.
Supplements and exercises
.126
Extensions of product measures
(126).
Measurability on products
(129).
Mařík
spaces
(130).
Separable measures
(132).
Diffused and
atomless
measures
(133).
Completion regular measures
(133).
Radon
spaces
(135).
Supports of measures
(136).
Generalizations of Lusin's
theorem
(137).
Metric outer measures
(140).
Capacities
(142).
Covariance operators and means of measures
(142).
The Choquet
representation
(145).
Convolution
(146).
Measurable linear
functions
(149).
Convex measures
(149).
Pointwise convergence
(151).
Infinite Radon measures
(154).
Exercises
(155).
Chapter
8.
Weak convergence of measure
.175
8.1.
The definition of weak convergence
.175
8.2.
Weak convergence of
nonnegative
measures
.182
8.3.
The case of metric space
.191
8.4.
Some properties of weak convergence
.194
8.5.
The Skorohod representation
.199
8.6.
Weak compactness and the Prohorov theorem
.202
8.7.
Weak sequential completeness
.209
8.8.
Weak convergence and the Fourier transform
.210
8.9.
Spaces of measures with the weak topology
.211
8.10.
Supplements and exercises
.217
Weak compactness
(217).
Prohorov spaces
(219).
The Weak sequential
completeness of spaces of measures
(226).
The
Л
-topology
(226).
Continuous mappings of spaces of measures
(227).
separability
of spaces of measures
(230).
Young measures
(231).
Metrics on
spaces of measures
(232).
Uniformly distributed sequences
(237).
Setwise convergence of measures
(241).
Stable convergence and
ws-topology
(246).
Exercises
(249)
Chapter
9.
Transformations of measures and isomorphisms
. 267
9.1.
Images and preimages of measures
.267
9.2.
Isomorphisms of measure spaces
.275
9.3.
Isomorphisms of measure algebras
.277
9.4.
Lebesgue Rohlin spaces
.280
9.5.
Induced point isomorphisms
.284
9.6.
Topologically equivalent measures
.286
9.7.
Continuous images of Lebesgue measure
.288
9.8.
Connections with extensions of measures
.291
9.9.
Absolute continuity of the images of measures
.292
9.10.
Shifts of measures along integral curves
.297
9.11.
Invariant measures and
Haar
measures
.303
9.12.
Supplements and exercises
.308
Projective
systems of measures
(308).
Extremal preimages of
measures and uniqueness
(310).
Existence of
atomless
measures
(317).
Invariant and quasi-invariant measures of transformations
(318).
Point
and Boolean isomorphisms
(320).
Almost homeomorphisms
(323).
Measures with given marginal projections
(324).
The Stone
representation
(325).
The Lyapunov theorem
(326).
Exercises
(329)
Chapter
10.
Conditional measures and conditional
expectations
.339
10.1.
Conditional expectations
.339
10.2.
Convergence of conditional expectations
.346
10.3.
Martingales
.348
10.4.
Regular conditional measures
.356
10.5.
Liftings and conditional measures
.371
10.6.
Disintegrations of measures
.380
10.7.
Transition measures
.384
10.8.
Measurable partitions
.389
10.9.
Ergodic theorems
.391
10.10.
Supplements and exercises
.398
Independence
(398).
Disintegrations
(403).
Strong liftings
(406).
Zero-one laws
(407).
Laws of large numbers
(410).
Gibbs
measures
(416).
Triangular mappings
(417).
Exercises
(427).
Bibliographical and Historical Comments
.439
References
.465
Author Index
.547
Subject Index
.561 |
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| author_facet | Bogačev, Vladimir I. 1961- |
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| author_sort | Bogačev, Vladimir I. 1961- |
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| building | Verbundindex |
| bvnumber | BV022397612 |
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| id | DE-604.BV022397612 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T17:17:05Z |
| indexdate | 2024-07-09T20:56:43Z |
| institution | BVB |
| isbn | 9783540345138 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015606326 |
| oclc_num | 315570181 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-573 DE-29T DE-20 DE-83 DE-188 DE-706 DE-739 DE-19 DE-BY-UBM |
| owner_facet | DE-824 DE-703 DE-573 DE-29T DE-20 DE-83 DE-188 DE-706 DE-739 DE-19 DE-BY-UBM |
| physical | xiii, 575 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Bogačev, Vladimir I. 1961- Verfasser (DE-588)121192318 aut Measure theory 2 V. I. Bogachev Berlin [u.a.] Springer [2007] xiii, 575 Seiten txt rdacontent n rdamedia nc rdacarrier Maßtheorie (DE-588)4074626-4 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 (DE-604)BV022397610 2 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015606326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bogačev, Vladimir I. 1961- Measure theory Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4074626-4 |
| title | Measure theory |
| title_auth | Measure theory |
| title_exact_search | Measure theory |
| title_exact_search_txtP | Measure theory |
| title_full | Measure theory 2 V. I. Bogachev |
| title_fullStr | Measure theory 2 V. I. Bogachev |
| title_full_unstemmed | Measure theory 2 V. I. Bogachev |
| title_short | Measure theory |
| title_sort | measure theory |
| topic | Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | Maßtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015606326&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022397610 |
| work_keys_str_mv | AT bogacevvladimiri measuretheory2 |