A guide to advanced real analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Washington, DC
Math. Assoc. of America
2009
|
| Series: | Dolciani mathematical expositions
37 MAA guides 2 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 107 S. graph. Darst. |
| ISBN: | 0883853434 9780883853436 |
Staff View
MARC
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| 245 | 1 | 0 | |a A guide to advanced real analysis |c Gerald B. Folland |
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Record in the Search Index
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| adam_text | Titel: A guide to advanced real analysis
Autor: Folland, Gerald B
Jahr: 2009
Contents
Preface......................................................... vü
Prologue: Notation, Terminology, and Set Theory................ 1
Numbers.............................. 1
Sets and mappings ........................ 2
Zorn s lemma........................... 3
1 Topology.................................................... 5
1.1 Metrie Spaces......................... 5
1.2 Topological Spaces and continuous maps .......... 9
1.3 Neighborhood bases and convergence............ 13
1.4 Compactness......................... 15
2 Measure and Integration: General Theory.................... 21
2.1 Measures........................... 21
2.2 Integration.......................... 26
2.3 Convergence of funetions and convergence of integrals ... 31
2.4 Product measures and the Fubini-Tonelli theorem...... 34
2.5 Relations between (signed and complex) measures..... 36
3 Measure and Integration: Constructions and Special Examples 41
3.1 Construction of measures .................. 41
3.2 Lebesgue measure...................... 44
3.3 Regulär Borel measures and funetions on the real line ... 52
3.4 Hausdorff measure...................... 56
3.5 Regulär Borel measures on LCH Spaces........... 59
4 Rudiments of Fnnctional Analysis............................ 63
4.1 Normed vector Spaces and bounded linear maps....... 63
4.2 Hubert spaces......................... 68
4.3 Other topological vector spaces............... 71
x Contents
5 Function Spaces............................................. 75
5.1 Lp spaces........................... 75
5.2 Spaces of continuous funetions ............... 80
6 Topics in Analysis on Euclidean Space........................ 85
6.1 Convolutions......................... 86
6.2 Fourier series and transforms................. 89
6.3 Distributions......................... 94
Bibliography...................................................101
Index...........................................................103
About the Author...............................................107
|
| any_adam_object | 1 |
| author | Folland, Gerald B. 1947- |
| author_GND | (DE-588)137062486 |
| author_facet | Folland, Gerald B. 1947- |
| author_role | aut |
| author_sort | Folland, Gerald B. 1947- |
| author_variant | g b f gb gbf |
| building | Verbundindex |
| bvnumber | BV036474874 |
| classification_rvk | SK 400 SK 430 SK 600 |
| classification_tum | MAT 260f |
| ctrlnum | (OCoLC)632958141 (DE-599)GBV608079715 |
| dewey-full | 515.8 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.8 |
| dewey-search | 515.8 |
| dewey-sort | 3515.8 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:40:16Z |
| institution | BVB |
| isbn | 0883853434 9780883853436 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020346491 |
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| physical | X, 107 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Math. Assoc. of America |
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| series | Dolciani mathematical expositions MAA guides |
| series2 | Dolciani mathematical expositions MAA guides |
| spelling | Folland, Gerald B. 1947- Verfasser (DE-588)137062486 aut A guide to advanced real analysis Gerald B. Folland Washington, DC Math. Assoc. of America 2009 X, 107 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Dolciani mathematical expositions 37 MAA guides 2 Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Analysis (DE-588)4001865-9 s Reelle Funktion (DE-588)4048918-8 s Maßtheorie (DE-588)4074626-4 s Integrationstheorie (DE-588)4138369-2 s Funktionalanalysis (DE-588)4018916-8 s DE-604 Dolciani mathematical expositions 37 (DE-604)BV001900740 37 MAA guides 2 (DE-604)BV035218151 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020346491&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Folland, Gerald B. 1947- A guide to advanced real analysis Dolciani mathematical expositions MAA guides Reelle Funktion (DE-588)4048918-8 gnd Maßtheorie (DE-588)4074626-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd Analysis (DE-588)4001865-9 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4048918-8 (DE-588)4074626-4 (DE-588)4018916-8 (DE-588)4001865-9 (DE-588)4138369-2 |
| title | A guide to advanced real analysis |
| title_auth | A guide to advanced real analysis |
| title_exact_search | A guide to advanced real analysis |
| title_full | A guide to advanced real analysis Gerald B. Folland |
| title_fullStr | A guide to advanced real analysis Gerald B. Folland |
| title_full_unstemmed | A guide to advanced real analysis Gerald B. Folland |
| title_short | A guide to advanced real analysis |
| title_sort | a guide to advanced real analysis |
| topic | Reelle Funktion (DE-588)4048918-8 gnd Maßtheorie (DE-588)4074626-4 gnd Funktionalanalysis (DE-588)4018916-8 gnd Analysis (DE-588)4001865-9 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Reelle Funktion Maßtheorie Funktionalanalysis Analysis Integrationstheorie |
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