Real analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Macmillan
1968
|
| Edition: | 2. ed. |
| Series: | Collier Macmillan international editions
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 349 S. |
| ISBN: | 0024041505 0029794102 |
Staff View
MARC
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| 245 | 1 | 0 | |a Real analysis |c H. L. Royden |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Macmillan |c 1968 | |
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Record in the Search Index
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Contents
Prologue to the Student 1
1 Set Theory 5
1 Introduction, 5
2 Functions, 8
3 Unions, intersections, and complements, 11
4 Algebras of sets, 16
5 The axiom of choice and infinite direct products, 18
6 Countable sets, 19
7 Relations and equivalences, 22
8 Partial orderings and the maximal principle, 23
9 We// ordering and the countable ordinals, 24
Part One o Theory of Functions of a Real Variable
2 The Real Number System 29
1 Axioms for the real numbers, 29
2 77ze natural and rational numbers as subsets of R, 32
3 The extended real numbers, 34
4 Sequences of real numbers, 35
5 O/wi 3/k/ closed sets of real numbers, 38
6 Continuous functions, 44
7 Bore/ .sett, 50
ix
x Contents
3 Lebesgue Measure 52
1 Introduction, 52
2 Outer measure, 54
3 Measurable sets and Lebesgue measure, 56
*4 A nonmeasurable set, 63
5 Measurable functions, 65
6 Littlewood's three principles, 71
4 The Lebesgue Integral 73
1 The Riemann integral, 73
2 7%e Lebesgue integral of a bounded function over a set of finite
measure, 75
3 The integral of a nonnegative function, 82
4 The general Lebesgue integral, 86
*5 Convergence in measure, 91
5 Differentiation and Integration 94
1 Differentiation of monotone functions, 94
2 Functions of bounded variation, 98
3 Differentiation of an integral, 101
4 Absolute continuity, 104
*5 Convex functions, 108
6 The Classical Banach Spaces 111
1 The V spaces, 111
2 7"fe Holder and Minkowski inequalities, 112
3 Convergence and completeness, 115
4 Bounded linear functionals on the V spaces, 119
Part Two d Abstract Spaces
7 Metric Spaces 127
1 Introduction, 127
2 O/?e/i and closed sets, 129
3 Continuous functions and homeomorphisms, 131
4 Convergence and completeness, 133
5 Uniform continuity and uniformity, 135
6 Subspaces, 137
7 ito/Ve category, 139
* Indicates sections peripheral to the principal line of argument.
Contents xi
8 Topological Spaces 142
1 Fundamental notions, 142
2 Bases and countability, 145
3 The separation axioms and continuous real valued functions, 147
4 Product spaces, 150
5 Connectedness, 150
*6 Absolute Qj's, 154
*7 Nets, 155
9 Compact Spaces 157
1 Basic properties, 157
2 Countable compactness and the Bolzano Weierstrassproperty, 159
3 Compact metric spaces, 163
4 Products of compact spaces, 165
5 Locally compact spaces, 168
*6 77ie Stone Cech compactification, 170
7 77te Stone Weierstrass theorem, 171
*8 r/ie ^sco/i theorem, 177
10 Banach Spaces 181
1 Introduction, 181
2 Linear operators, 184
3 Linear functionals and the Hahn Banach theorem, 186
4 77ie closed graph theorem, 193
*5 Topological vector spaces, 197
*6 Wea/t topologies, 200
*7 Convexity, 203
8 /ft/for? space, 210
Part Three a General Measure and Integration Theory
11 Measure and Integration 217
1 Measure spaces, 217
2 Measurable functions, 223
3 Integration, 225
*4 General convergence theorems, 231
5 Signed measures, 232
6 7"Ae Radon Nikodym theorem, 238
7 77/e Lp spaces, 243
xii Contents
12 Measure and Outer Measure 250
1 Outer measure and measurability, 250
2 The extension theorem, 253
*3 The Lebesgue Stieltjes integral, 261
4 Product measures, 264
*5 Inner measure, 274
*6 Extension by sets of measure zero, 281
*7 Caratheodory outer measure, 283
13 The Daniell Integral 286
1 Introduction, 286
2 The extension theorem, 288
3 Uniqueness, 294
4 Measurability and measure, 295
14 Measure and Topology 301
1 Baire sets and Borel sets, 301
2 Positive linear functionals and Baire measures, 304
3 Bounded linear functionals on C(X), 308
*4 The Borel extension of a measure, 313
15 Mappings of Measure Spaces 317
1 Point mappings and set mappings, 317
2 Measure algebras, 319
3 Borel equivalences, 324
4 5W mappings and point mappings on complete metric spaces, 328
5 The isometries of Lp, 331
Epilogue 335
Bibliography 337
Index of Symbols 339
Subject Index 341 |
| any_adam_object | 1 |
| author | Royden, Halsey L. 1928-1993 |
| author_GND | (DE-588)172349532 |
| author_facet | Royden, Halsey L. 1928-1993 |
| author_role | aut |
| author_sort | Royden, Halsey L. 1928-1993 |
| author_variant | h l r hl hlr |
| building | Verbundindex |
| bvnumber | BV002656488 |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)318332850 (DE-599)BVBBV002656488 |
| 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 |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV002656488 |
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| indexdate | 2025-03-25T13:00:42Z |
| institution | BVB |
| isbn | 0024041505 0029794102 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001703243 |
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| physical | XII, 349 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | Macmillan |
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| spelling | Royden, Halsey L. 1928-1993 Verfasser (DE-588)172349532 aut Real analysis H. L. Royden 2. ed. New York [u.a.] Macmillan 1968 XII, 349 S. txt rdacontent n rdamedia nc rdacarrier Collier Macmillan international editions Análisis matemático Cálculo Funciones de variable real embne Reelle Funktion (DE-588)4048918-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Reelle Variable (DE-588)4202614-3 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Analysis (DE-588)4001865-9 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Reelle Variable (DE-588)4202614-3 s Funktionalanalysis (DE-588)4018916-8 s Maßtheorie (DE-588)4074626-4 s 1\p DE-604 Reelle Funktion (DE-588)4048918-8 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703243&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Royden, Halsey L. 1928-1993 Real analysis Análisis matemático Cálculo Funciones de variable real embne Reelle Funktion (DE-588)4048918-8 gnd Funktionalanalysis (DE-588)4018916-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Maßtheorie (DE-588)4074626-4 gnd Analysis (DE-588)4001865-9 gnd Reelle Variable (DE-588)4202614-3 gnd |
| subject_GND | (DE-588)4048918-8 (DE-588)4018916-8 (DE-588)4071510-3 (DE-588)4074626-4 (DE-588)4001865-9 (DE-588)4202614-3 (DE-588)4151278-9 |
| title | Real analysis |
| title_auth | Real analysis |
| title_exact_search | Real analysis |
| title_full | Real analysis H. L. Royden |
| title_fullStr | Real analysis H. L. Royden |
| title_full_unstemmed | Real analysis H. L. Royden |
| title_short | Real analysis |
| title_sort | real analysis |
| topic | Análisis matemático Cálculo Funciones de variable real embne Reelle Funktion (DE-588)4048918-8 gnd Funktionalanalysis (DE-588)4018916-8 gnd Funktion Mathematik (DE-588)4071510-3 gnd Maßtheorie (DE-588)4074626-4 gnd Analysis (DE-588)4001865-9 gnd Reelle Variable (DE-588)4202614-3 gnd |
| topic_facet | Análisis matemático Cálculo Funciones de variable real Reelle Funktion Funktionalanalysis Funktion Mathematik Maßtheorie Analysis Reelle Variable Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001703243&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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