Advanced analysis: on the real line
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1996
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | IX, 259 S. |
| ISBN: | 038794642X 9780387946429 |
Internformat
MARC
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| 100 | 1 | |a Kannan, Rangachary |e Verfasser |0 (DE-588)114601518 |4 aut | |
| 245 | 1 | 0 | |a Advanced analysis |b on the real line |c R. Kannan ; Carole King Krueger |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a IX, 259 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Mathematical analysis | |
| 650 | 4 | |a Functions of real variables | |
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| 700 | 1 | |a Krueger, Carole King |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1807228600462606336 |
|---|---|
| adam_text |
Contents
Preface v
Chapter 0 Preliminaries 1
0.1 Lebesgue Measure 1
0.2 The Lebesgue Integral 7
0.3 Vitali Covering Theorem 10
0.4 Baire Category Theorem and Baire Class Functions 18
Chapter 1 Monotone Functions 19
1.1 Continuity Properties 19
1.2 Differentiability Properties 22
1.3 Reconstruction of/ from /' 25
1.4 Series of Monotone Functions 31
Exercises 33
Chapter 2 Density and Approximate Continuity 37
2.1 Preliminaries and Definitions 37
2.2 The Lebesgue Density Theorem 40
2.3 Approximate Continuity 43
2.4 Approximate Continuity and Integrability 46
2.5 Further Results on Approximate Continuity 48
2.6 Sierpinski's Theorem 49
2.7 The Darboux Property and the Density Topology 50
Exercises 52
Chapter 3 Dini Derivatives 55
3.1 Preliminaries and Definitions 55
vii
viii Contents
3.2 Simple Properties of Derivatives 58
3.3 Ruziewicz's Example 60
3.4 Further Properties of Derivatives 62
3.5 The Denjoy Saks Young Theorem 67
3.6 Measurability of Dini Derivatives 71
3.7 Dini Derivatives and Convex Functions 74
Exercises 76
Chapter 4 Approximate Derivatives 81
4.1 Definitions 81
4.2 Measurability of Approximate Derivatives 82
4.3 Analogue of the Denjoy Saks Young Theorem 85
4.4 Category Results for Approximate Derivatives 88
4.5 Other Properties of Approximate Derivatives 98
Exercises 101
Chapter 5 Additional Results on Derivatives 102
5.1 Derivatives 102
5.2 Derivates 103
5.3 Approximate Derivatives 105
5.4 The Denjoy Property 112
5.5 Metrically Dense 114
Chapter 6 Bounded Variation 118
6.1 Bounded Variation of Finite Intervals 118
6.2 Stieltjes Integral 131
6.3 The Space BF[a,b] 136
6.4 BVl0C and L^ 140
6.5 Additional Remarks on Fubini's Theorem 147
Exercises 148
Chapter 7 Absolute Continuity 153
7.1 Absolute Continuity 153
7.2 Rectifiable Curves 173
Exercises 178
Chapter 8 Cantor Sets and Singular Functions 181
8.1 The Cantor Ternary Set and Function 181
8.2 Hausdorff Measure 189
8.3 Generalized Cantor Sets—Part I 196
8.4 Generalized Cantor Sets—Part II 197
8.5 Cantor like Sets 199
8.6 Strictly Increasing Singular Functions 208
Exercises 213
Contents ix
Chapter 9 Spaces of BV and AC Functions 216
9.1 Convergence in Variation 216
9.2 Convergence in Length 220
9.3 Norms on AC 228
9.4 Norms on BV 237
Chapter 10 Metric Separability 246
Exercises 251
Bibliography 253
Index 257 |
| any_adam_object | 1 |
| author | Kannan, Rangachary Krueger, Carole King |
| author_GND | (DE-588)114601518 |
| author_facet | Kannan, Rangachary Krueger, Carole King |
| author_role | aut aut |
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| building | Verbundindex |
| bvnumber | BV010937775 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300.K35 1996 |
| callnumber-search | QA300.K35 1996 |
| callnumber-sort | QA 3300 K35 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 400 |
| ctrlnum | (OCoLC)246928484 (DE-599)BVBBV010937775 |
| dewey-full | 515/.820 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.8 20 |
| dewey-search | 515/.8 20 |
| dewey-sort | 3515 18 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010937775 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-13T00:04:59Z |
| institution | BVB |
| isbn | 038794642X 9780387946429 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007316540 |
| oclc_num | 246928484 |
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| owner_facet | DE-355 DE-BY-UBR DE-29T DE-739 DE-824 DE-20 DE-521 DE-19 DE-BY-UBM DE-11 DE-706 |
| physical | IX, 259 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Kannan, Rangachary Verfasser (DE-588)114601518 aut Advanced analysis on the real line R. Kannan ; Carole King Krueger New York [u.a.] Springer 1996 IX, 259 S. txt rdacontent n rdamedia nc rdacarrier Universitext Hier auch später erschienene, unveränderte Nachdrucke Mathematical analysis Functions of real variables Analysis (DE-588)4001865-9 gnd rswk-swf Analysis (DE-588)4001865-9 s DE-604 Krueger, Carole King Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007316540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kannan, Rangachary Krueger, Carole King Advanced analysis on the real line Mathematical analysis Functions of real variables Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4001865-9 |
| title | Advanced analysis on the real line |
| title_auth | Advanced analysis on the real line |
| title_exact_search | Advanced analysis on the real line |
| title_full | Advanced analysis on the real line R. Kannan ; Carole King Krueger |
| title_fullStr | Advanced analysis on the real line R. Kannan ; Carole King Krueger |
| title_full_unstemmed | Advanced analysis on the real line R. Kannan ; Carole King Krueger |
| title_short | Advanced analysis |
| title_sort | advanced analysis on the real line |
| title_sub | on the real line |
| topic | Mathematical analysis Functions of real variables Analysis (DE-588)4001865-9 gnd |
| topic_facet | Mathematical analysis Functions of real variables Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007316540&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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