Integration theory: a second course
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 277 S. |
| ISBN: | 9812381155 |
Staff View
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Record in the Search Index
| _version_ | 1804129619309232128 |
|---|---|
| adam_text | Contents
Preface
v
Part
1:
Basic
Integration Theory
1
Overview
3
1.
Abstract Integration
5
1.1
Basic Notions
.......................... 5
1.2
Measurable Functions
..................... 10
1.3
Definition of the Integral and Convergence Theorems
.... 38
1.4
Extension of Measures
..................... 64
1.5
Product Measures and Fubini s Theorem
........... 75
1.6
Exercises
............................ 89
2.
Adding a Topological Structure: The Radon Measure
95
2.1
Preliminaries from Topology
.................. 95
2.2
Borei
Measures and Luzin s Theorem
............. 108
2.3
Radon Measures
........................ 113
2.4
Exercises
............................ 125
3.
Adding a Group Structure: The
Haar
Measure
129
3.1
Preliminaries from Topological Groups
............ 129
3.2
The
Haar
Measure
....................... 132
3.3
Exercises
............................ 149
vii
viii Contents
Part
2:
Advanced Topics
151
4.
Spaces of Measurable Functions
153
4.1
Lp Spaces
............................ 153
4.2
Ideal Spaces
........................... 156
4.3
Dual Spaces
........................... 167
4.4
Exercises
............................ 178
5.
Convolutions
183
5.1
The Modular Function
..................... 183
5.2
Convolutions
.......................... 190
5.3
Exercises
............................ 198
6.
Connections with Logic and Set Theory
201
6.1
The Axiom of Choice and the Continuum Hypothesis
.... 201
6.2
The Banach-Tarski Paradox
.................. 213
6.3
Consequences on Measure Theory
............... 217
6.4
Exercises
............................ 229
7.
Special Properties of the Lebesgue Measure
233
7.1
Connections with the Riemann Integral
........... 233
7.2
The Fundamental Theorem of Calculus
............ 237
7.3
Exercises
............................ 247
8.
Miscellaneous
249
8.1
Some Useful Formulas
..................... 249
8.2
The Graph of a Function and Rearrangements
....... 255
8.3
Exercises
............................ 263
Bibliography
265
Index
269
|
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:08:01Z |
| institution | BVB |
| isbn | 9812381155 |
| language | English |
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| physical | VIII, 277 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | World Scientific |
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| spelling | Väth, Martin 1967- Verfasser (DE-588)115361499 aut Integration theory a second course Martin Väth New Jersey [u.a.] World Scientific 2002 VIII, 277 S. txt rdacontent n rdamedia nc rdacarrier Integrationstheorie Integration Mathematik (DE-588)4072852-3 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 s DE-604 Integration Mathematik (DE-588)4072852-3 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Väth, Martin 1967- Integration theory a second course Integrationstheorie Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4072852-3 (DE-588)4138369-2 |
| title | Integration theory a second course |
| title_auth | Integration theory a second course |
| title_exact_search | Integration theory a second course |
| title_full | Integration theory a second course Martin Väth |
| title_fullStr | Integration theory a second course Martin Väth |
| title_full_unstemmed | Integration theory a second course Martin Väth |
| title_short | Integration theory |
| title_sort | integration theory a second course |
| title_sub | a second course |
| topic | Integrationstheorie Integration Mathematik (DE-588)4072852-3 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Integrationstheorie Integration Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010047603&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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