An introduction to measure theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2011
|
| Schriftenreihe: | Graduate studies in mathematics
126 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XVI, 206 S. |
| ISBN: | 9780821869192 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804148479842320384 |
|---|---|
| adam_text | Contents
Preface
ix
Notation
x
Acknowledgments
xv
Chapter
1.
Measure theory
1
§1.1.
Prologue: The problem of measure
2
§1.2.
Lebesgue measure
15
§1.3.
The Lebesgue integral
38
§1.4.
Abstract measure spaces
66
§1.5.
Modes of convergence
94
§1.6.
Differentiation theorems
108
§1.7.
Outer measures, pre-measures, and product measures
148
Chapter
2.
Related articles
173
§2.1.
Problem solving strategies
174
§2.2.
The Rademacher differentiation theorem
187
§2.3.
Probability spaces
192
§2.4.
Infinite product spaces and the Kolmogorov extension
theorem
194
Bibliography
201
Index
203
VII
This is a graduate text introducing the fundamentals of measure
theory and integration theory, which is the foundation of modern
real analysis. The text focuses first on the concrete setting of
Lebesgue measure and the Lebesgue integral (which in turn is
motivated by the more classical concepts of Jordan measure and
the Riemann integral), before moving on to abstract measure and
integration theory, including the standard convergence theorems,
Fubini s theorem, and the
Carathéodory
extension theorem.
Classical differentiation theorems, such as the Lebesgue and
Rademacher differentiation theorems, are also covered, as are connections with
probability theory. The material is intended to cover a quarter or semester s worth
of material for a first graduate course in real analysis.
There is an emphasis in the text on tying together the abstract and the concrete
sides of the subject, using the latter to illustrate and motivate the former. The central
role of key principles (such as Littlewood s three principles) as providing guiding
intuition to the subject is also emphasized. There are a large number of exercises
throughout that develop key aspects of the theory, and are thus an integral compo¬
nent of the text.
As a supplementary section, a discussion of general problem-solving strategies in
analysis is also given. The last three sections discuss optional topics related to the
main matter of the book.
|
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| discipline | Mathematik |
| format | Book |
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| institution | BVB |
| isbn | 9780821869192 |
| language | English |
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| physical | XVI, 206 S. |
| publishDate | 2011 |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut An introduction to measure theory Terence Tao Providence, RI American Math. Soc. 2011 XVI, 206 S. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 126 Hier auch später erschienene, unveränderte Nachdrucke Maßtheorie (DE-588)4074626-4 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s DE-604 Graduate studies in mathematics 126 (DE-604)BV009739289 126 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024479848&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024479848&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Tao, Terence 1975- An introduction to measure theory Graduate studies in mathematics Maßtheorie (DE-588)4074626-4 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4138369-2 (DE-588)4123623-3 |
| title | An introduction to measure theory |
| title_auth | An introduction to measure theory |
| title_exact_search | An introduction to measure theory |
| title_full | An introduction to measure theory Terence Tao |
| title_fullStr | An introduction to measure theory Terence Tao |
| title_full_unstemmed | An introduction to measure theory Terence Tao |
| title_short | An introduction to measure theory |
| title_sort | an introduction to measure theory |
| topic | Maßtheorie (DE-588)4074626-4 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Maßtheorie Integrationstheorie Lehrbuch |
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