Measure theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York ; Heidelberg ; Berlin
Springer
1974
|
| Schriftenreihe: | Graduate texts in mathematics
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xi, 304 Seiten |
| ISBN: | 0387900888 3540900888 9781468494426 |
Internformat
MARC
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| 100 | 1 | |a Halmos, Paul R. |d 1916-2006 |0 (DE-588)118746677 |4 aut | |
| 245 | 1 | 0 | |a Measure theory |c Paul R. Halmos |
| 264 | 1 | |a New York ; Heidelberg ; Berlin |b Springer |c 1974 | |
| 300 | |a xi, 304 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 18 | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a matematika - analiza - teorija mere - učbeniki za visoke šole | |
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| 689 | 1 | 0 | |a Messtheorie |0 (DE-588)4169537-9 |D s |
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| 830 | 0 | |a Graduate texts in mathematics |v 18 |w (DE-604)BV000000067 |9 18 | |
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Datensatz im Suchindex
| _version_ | 1805076913019944960 |
|---|---|
| adam_text |
CONTENTS
PAGE
Preface
.
v
Acknowledgments
.
vii
SECTION
0.
Prerequisites
. 1
CHAPTER I: SETS AND CLASSES
1.
Set inclusion
. 9
2.
Unions and intersections
. 11
3.
Limits, complements, and differences
. 16
4.
Rings and algebras
. 19
5.
Generated rings and
σ
-rings
.
22
6.
Monotone classes
. 26
CHAPTER
И:
MEASURES AND OUTER MEASURES
7.
Measure on rings
. 30
8.
Measure on intervals
. 32
9.
Properties of measures
. 37
10.
Outer measures
. 41
11.
Measurable sets
. 44
CHAPTER III: EXTENSION OF MEASURES
12.
Properties of induced measures
. 49
13.
Extension, completion, and approximation
. 54
14.
Inner measures
. 58
15
Lebesgue measure
. 62
16.
Non
measurable sets
. 67
chapter
iv:
measurable functions
17.
Measure spaces
. 73
18.
Measurable functions
. 76
SECTIOK PAGE
19.
Combinations of measurable functions
. 80
20.
Sequences of measurable functions
. 84
21.
Pointwise convergence
. 86
22.
Convergence in measure
.
SO
CHAPTER V: INTEGRATION
23.
Integrable
simple functions
. 95
24.
Sequences of
integrable
simple functions
. 98
25.
Integrable
functions
. 102
26.
Sequences of
integrable
functions
. 107
27.
Properties of integrals
. 112
chapter
vi:
general set functions
28.
Signed measures
. 117
29. Hahn
and Jordan decompositions
. 120
30.
Absolute continuity
. 124
31.
The Radon-Nikodym theorem
. 128
32.
Derivatives of signed measures
.·. 132
chapter
vii:
product spaces
33.
Cartesian products
. 137
34.
Sections
. 141
35.
Product measures
. 143
36.
Fubini's theorem
. 145
37.
Finite dimensional product spaces
. 150
38.
Infinite dimensional product spaces
. 154
CHAPTER Vni: TRANSFORMATIONS AND FUNCTIONS
39.
Measurable transformations
. 161
40.
Measure rings
. 165
41.
The isomorphism theorem
. 171
42.
Function spaces
. 174
43.
Set functions and point functions
. 178
chapter
ix:
probability
44.
Heuristic introduction
. 184
45.
Independence
. 191
46.
Series of independent functions
. 196
SECTION PAOK
47.
The law of
large
numbers.
201
48.
Conditional probabilities and expectations
. 206
49.
Measures on product spaces
. 211
CHAPTER X: LOCALLY COMPACT SPACES
50.
Topological lemmas
. 216
51.
Borei
sets and Baire sets
. 219
52.
Regular measures
. 223
53.
Generation of
Borei
measures
. 231
54.
Regular contents
. 237
55.
Classes of continuous functions
. 240
56.
Linear
funcţionale
. 243
chapter
xi:
haar
measure
57.
Full subgroups
. 250
58.
Existence
. 251
59.
Measurable groups
. 257
60.
Uniqueness
. 262
chapter
xii:
measure and topology in groups
61.
Topology in terms of measure
. 266
62.
Weil topology
. 270
63.
Quotient groups
. 277
64.
The regularity of
Haar
measure
. 282
References
. 291
Bibliography
. 293
List of frequently used symbols
. 297
Index
. 299 |
| any_adam_object | 1 |
| author | Halmos, Paul R. 1916-2006 |
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| author_sort | Halmos, Paul R. 1916-2006 |
| author_variant | p r h pr prh |
| building | Verbundindex |
| bvnumber | BV006293831 |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)443636078 (DE-599)BVBBV006293831 |
| discipline | Mathematik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:04:51Z |
| institution | BVB |
| isbn | 0387900888 3540900888 9781468494426 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003979270 |
| oclc_num | 443636078 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-20 DE-703 DE-355 DE-BY-UBR DE-473 DE-BY-UBG DE-824 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-29T DE-92 DE-19 DE-BY-UBM DE-1046 DE-634 DE-83 DE-11 DE-188 DE-898 DE-BY-UBR DE-521 |
| physical | xi, 304 Seiten |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Halmos, Paul R. 1916-2006 (DE-588)118746677 aut Measure theory Paul R. Halmos New York ; Heidelberg ; Berlin Springer 1974 xi, 304 Seiten txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 18 Hier auch später erschienene, unveränderte Nachdrucke matematika - analiza - teorija mere - učbeniki za visoke šole Messtheorie (DE-588)4169537-9 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Maßtheorie (DE-588)4074626-4 s DE-604 Messtheorie (DE-588)4169537-9 s Erscheint auch als Online-Ausgabe 978-1-4684-9440-2 Graduate texts in mathematics 18 (DE-604)BV000000067 18 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003979270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Halmos, Paul R. 1916-2006 Measure theory Graduate texts in mathematics matematika - analiza - teorija mere - učbeniki za visoke šole Messtheorie (DE-588)4169537-9 gnd Maßtheorie (DE-588)4074626-4 gnd |
| subject_GND | (DE-588)4169537-9 (DE-588)4074626-4 (DE-588)4151278-9 |
| title | Measure theory |
| title_auth | Measure theory |
| title_exact_search | Measure theory |
| title_full | Measure theory Paul R. Halmos |
| title_fullStr | Measure theory Paul R. Halmos |
| title_full_unstemmed | Measure theory Paul R. Halmos |
| title_short | Measure theory |
| title_sort | measure theory |
| topic | matematika - analiza - teorija mere - učbeniki za visoke šole Messtheorie (DE-588)4169537-9 gnd Maßtheorie (DE-588)4074626-4 gnd |
| topic_facet | matematika - analiza - teorija mere - učbeniki za visoke šole Messtheorie Maßtheorie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003979270&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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