Modern theories of integration
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Dover
1960
|
| Ausgabe: | 2., rev. ed. |
| Schriftenreihe: | Dover books on advanced mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Kestelman, Hyman |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Modern theories of integration |c by H. Kestelman |
| 250 | |a 2., rev. ed. | ||
| 264 | 1 | |a New York |b Dover |c 1960 | |
| 300 | |a X, 308 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Dover books on advanced mathematics | |
| 650 | 4 | |a Intégrales généralisées | |
| 650 | 4 | |a Integrals, Generalized | |
| 650 | 0 | 7 | |a Integrationstheorie |0 (DE-588)4138369-2 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0102 MAT 280f 2001 A 20547 |
|---|---|
| DE-BY-TUM_katkey | 496890 |
| DE-BY-TUM_location | 01 |
| DE-BY-TUM_media_number | 040010424841 |
| _version_ | 1820882395522400256 |
| adam_text | CONTENTS
I. SETS OF POINTS ...... 1
§ 1. Real numbers ...... 1
§ 2. Sets of points ...... 2
§ 3. Equivalence of aggregates . . . . 8
§4. Metrical properties of Rn. . . . .13
§ 5. The Selection Axiom . . . . .28
§ 6. General Principle of Convergence in Rn . . .29
II. RIEMANN INTEGRATION . . . . .30
§1. Functions defined in a set of points . . .30
§ 2. Definition of Riemann integral . . . .32
§ 3. Conditions for a function to be integrable-iJ . . 36
§ 4. Properties of the Riemann integral . . .42
§ 5. Riemann integration of derivatives . . .46
§ 6. Riemann integration of limit functions . . .50
§ 7. Cauchy-Riemann integral . . .54
§ 8. Geometric interpretation of Riemann integration. . 55
III. LEBESGUE MEASURE . . . . .67
§ 1. Exterior Lebesgue measure . . . .67
§ 2. Measurable sets . . . . . .70
§ 3. Interior Lebesgue measure . . . .80
§ 4. Linear transformations . . . . .87
§ 5. Non-measurable sets . . . . .89
IV. SETS OF ORDINATES AND MEASURABLE FUNCTIONS 92
§ 1. Sets of ordinates . . . . . .92
§ 2. Cylinder sets . . . . . .94
§ 3. Measurable functions . . . . .96
§ 4. Lusin s theorem ...... 109
V. LEBESGUE INTEGRAL OF A NON-NEGATIVE FUNCTION 113
VI. LEBESGUE INTEGRALS OF FUNCTIONS WHICH ARE
SOMETIMES NEGATIVE . . . .128
§ 1. Real functions . . . . . .128
§ 2. Complex functions ..... 156
VII. FUNCTIONS OF A SINGLE VARIABLE . . .161
§ 1. Miscellaneous theorems: integration by parts, second mean-
value theorem, differentiation under the integral sign . 161
§ 2. Derivative of a Lebesgue integral . . .172
§ 3. Summability of derivatives .... 174
§ 4. Bounded variation and absolute continuity . .184
§ 5. Integration by substitution .... 192
§ 6. Appendix to § 3 . . . . . .199
VIII. EVALUATION OF DOUBLE INTEGRALS . . .202
x CONTENTS
IX. EXTENSIONS OF THE LEBESGUE INTEGRAL . .213
§ 1. Holder-Lebesgue integral . . . .213
§ 2. General Denjoy integral ..... 217
X. FOURIER SERIES . . . . . .228
§ 1. Introduction ...... 228
§ 2. Convergence tests ..... 232
§ 3. Summability (C, 1) of Fourier series . . . 240
§4. Integration of Fourier series . . . .241
§ 5. Trigonometric and Fourier series. . . . 243
XI. RIEMANN-STIELTJES INTEGRATION . . .247
§ 1. Introduction . . . . . .247
§ 2. The Riemann-Stieltjes integral .... 248
§ 3. Properties of the Riemann-Stieltjes integral . . 251
§ 4. Applications of Stieltjes integration . . . 262
§ 5-. Riesz s theorem ...... 265
EXERCISES . . . . . . .270
BIBLIOGRAPHY . . . . . .303
INDEX OF DEFINITIONS AND SYMBOLS . . .304
GENERAL INDEX . . . . . .306
INDEX TO THE EXERCISES . . . .309
SET-THEORY NOTATION
The principal differences between the notation in the text and that
in current use are noted below. The intersection AB is now usually
denoted by A n B and UAr by j | Ar. Similarly A+B and A + B
t r
may be denoted by A U B and £4r by JAr. The symbol A is now
r r
generally used to denote the closure of A, i.e. A U A (denoted in the
text by Ac [def.2O]); the complement of A (denoted in the text by
A) is then denoted by C(A).
|
| any_adam_object | 1 |
| author | Kestelman, Hyman |
| author_facet | Kestelman, Hyman |
| author_role | aut |
| author_sort | Kestelman, Hyman |
| author_variant | h k hk |
| building | Verbundindex |
| bvnumber | BV003713242 |
| callnumber-first | Q - Science |
| callnumber-label | QA312 |
| callnumber-raw | QA312 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)253461 (DE-599)BVBBV003713242 |
| dewey-full | 517.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 517 - [Unassigned] |
| dewey-raw | 517.3 |
| dewey-search | 517.3 |
| dewey-sort | 3517.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2., rev. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-23T11:03:45Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002363535 |
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| physical | X, 308 S. |
| publishDate | 1960 |
| publishDateSearch | 1960 |
| publishDateSort | 1960 |
| publisher | Dover |
| record_format | marc |
| series2 | Dover books on advanced mathematics |
| spellingShingle | Kestelman, Hyman Modern theories of integration Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4138369-2 |
| title | Modern theories of integration |
| title_auth | Modern theories of integration |
| title_exact_search | Modern theories of integration |
| title_full | Modern theories of integration by H. Kestelman |
| title_fullStr | Modern theories of integration by H. Kestelman |
| title_full_unstemmed | Modern theories of integration by H. Kestelman |
| title_short | Modern theories of integration |
| title_sort | modern theories of integration |
| topic | Intégrales généralisées Integrals, Generalized Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Intégrales généralisées Integrals, Generalized Integrationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002363535&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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