Lectures on measure and integration: by Harold Widom. Notes by David Drasin and Anthony J.Tromba
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Van Nostrand Reinhold
1969
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| Series: | Van Nostrand mathematical studies
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII,166 S. |
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Record in the Search Index
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| adam_text | LECTURES ON MEASURE AND INTEGRATION BY HAROLD WIDOM UNIVERSITY OF
CALIFORNIA, SANTA CRUZ DAVID DRASIN PURDUE UNIVERSITY NOTES BY ANTHONY
J. TROMBA STANFORD UNIVERSITY FOCHBEREICH MATHEMATIK DARMSTADT
MATHEMATIK - VAN NOSTRAND REINHOLD COMPANY NEW YORK CINCINNATI TORONTO
LONDON MELBOURNE TABLE OF CONTENTS CHAPTER I: MEASURES DEFINITION OF
MEASURE 3; REGULAR MEASURE 4; OUTER MEASURE 6; MEASURABLE SET 8; HAHN
EXTENSION THEOREM 10; MONOTONE FAMILIES OF SETS 12; COMPLETION OF
MEASURES 14; BOREL SETS AND CONSTRUC- TION OF LEBESGUE MEASURE IN THE
REAL LINE 15; THE CANTOR SET 16; A NON-MEASURABLE SET 16. CHAPTER II:
INTEGRATION MEASURE SPACES AND MEASURABLE FUNCTIONS 19; DEFINITION OF
THE INTEGRAL FOR NON-NEGATIVE FUNCTIONS 22; THE INTEGRAL AS A MEASURE
23; LINEARITY OF THE INTEGRAL 25; MONOTONE CONVERGENCE THEOREM 28;
FATOU S LEMMA 30; THE INTEGRAL FOR REAL-VALUED FUNCTIONS 32; THE
INTEGRAL FOR COMPLEX-VALUED FUNCTIONS 33; DOMINATED CONVERGENCE THEOREM
34; BOUNDED CONVERGENCE THEOREM 35; EGOROFF S THEOREM 36; CONVERGENCE IN
MEASURE 37; L -CONVERGENCE 39; THE LEBESGUE AND RIEMANN INTEGRALS 41.
CHAPTER III: THE THEOREMS OF FUBINI DEFINITION OF X X ^ 45; SIMPLE
FUNCTIONS 49; INTERCHANGE OF INTEGRATION FOR NON -NEGATIVE FUNCTIONS 51;
INTERCHANGE OF INTEGRA- TION FOR LJ FUNCTIONS 51* COMPLETION OF X X II
52; A THEOREM ON CHANGE OF VARIABLES IN INTEGRATION 54. CHAPTER IV:
REPRESENTATIONS OF MEASURES DEFINITION OF P 58; JORDAN DECOMPOSITION
THEOREM 60; HAHN DECOMPOSITION THEOREM 62; THE INTEGRAL FOR COMPLEX
MEASURES 64; VN VIII NOTES ON MEASURE AND INTEGRA TION FUNCTIONS OF
BOUNDED VARIATION 64; THE CANTOR FUNCTION 66; ABSO- LUTELY CONTINUOUS
MEASURES 67; RADON-NIKODYN THEOREM 69; THE RADON-NIKODYN DERIVATIVE 73;
MUTUALLY SINGULAR MEASURES 73; LEBESGUE DECOMPOSITION THEOREM 74;
CHAPTER V: THE LEBESGUE SPACES HOLDER S INEQUALITY 79; COMPLETENESS OF L
81; FUNCTIONS ON REGULAR MEASURE SPACES 84; CONTINUITY OF TRANSLATION IN
L NORM 85; CONTINUOUS LINEAR FUNCTIONALS 86; WEAK AND STRONG CONVERGENCE
OF FUNCTIONALS 88; THE DUAL SPACES OF L 91; THE DUAL SPACE OF CQ(S) 95.
CHAPTER VI: DIFFERENTIATION DERIVATIVE OF A MEASURELO7; VITALI COVERING
THEOREM 108; UPPER AND LOWER DERIVATES 110; REGULARITY OF FINITE BOREL
MEASURES 111; EXISTENCE OF D/X(X) A.E. 114; CONVERGENCE OF MEASURES 116;
POINTS OF DENSITY AND DISPERSION 117; DIFFERENTIATION OF INTEGRALS 118;
DIF- FERENTIATION OF SINGULAR MEASURES 119; THE LEBESGUE SET 120; INTE-
GRATION BY PARTS 122. CHAPTER VII: FOURIER SERIES ORTHOGONAL SYSTEMS OF
FUNCTIONS 123; DEFINITION OF FOURIER SERIES AND FOURIER COEFFICIENTS
125; BESSEL S INEQUALITY 126; RIESZ- FISCHER THEOREM 127; COMPLETE
SYSTEMS 128; COMPLETENESS OF EX- PONENTIAL AND TRIGONOMETRIC SYSTEMS
129; POISSON KERNEL 132; POSI- TIVE KERNELS 136; RIEMANN-LEBESGUE
THEOREM 139; THE KERNEL D (U) 141; DIRICHLET-JORDAN THEOREM 142;
INTEGRATION OF FOURIER SERIES 147; ABEL SUMMABILITY OF FOURIER SERIES
149; (C, 1) SUMMABILITY OF FOURIE SERIES 149; (C, 1) SUMMABILITY OF
FOURIER SERIES ON LI 151; A CON- TINUOUS FUNCTION WHOSE FOURIER SERIES
DIVERGES AT 0 153; UNIFORM BOUNDEDNESS THEOREM 156; L CONVERGENCE OF
FOURIER SERIES 157; M. RIESZ INTERPOLATION THEOREM 163; HAUSDORFF-YOUNG
THEOREM 166.
|
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| author | Widom, Harold 1932-2021 |
| author_GND | (DE-588)119159570 (DE-588)142684996 |
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| author_sort | Widom, Harold 1932-2021 |
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| building | Verbundindex |
| bvnumber | BV003166431 |
| classification_rvk | SK 430 |
| ctrlnum | (OCoLC)622780625 (DE-599)BVBBV003166431 |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:54:38Z |
| institution | BVB |
| language | English |
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| physical | VIII,166 S. |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Van Nostrand Reinhold |
| record_format | marc |
| series | Van Nostrand mathematical studies |
| series2 | Van Nostrand mathematical studies |
| spelling | Widom, Harold 1932-2021 Verfasser (DE-588)119159570 aut Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba New York [u.a.] Van Nostrand Reinhold 1969 VIII,166 S. txt rdacontent n rdamedia nc rdacarrier Van Nostrand mathematical studies 20 Integrals, Generalized Measure Theory Maßtheorie (DE-588)4074626-4 gnd rswk-swf Integrationstheorie (DE-588)4138369-2 gnd rswk-swf Maßtheorie (DE-588)4074626-4 s DE-604 Integrationstheorie (DE-588)4138369-2 s Drasin, David Sonstige oth Tromba, Anthony J. 1943- Sonstige (DE-588)142684996 oth Van Nostrand mathematical studies 20 (DE-604)BV021856926 20 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001986942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Widom, Harold 1932-2021 Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba Van Nostrand mathematical studies Integrals, Generalized Measure Theory Maßtheorie (DE-588)4074626-4 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| subject_GND | (DE-588)4074626-4 (DE-588)4138369-2 |
| title | Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| title_auth | Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| title_exact_search | Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| title_full | Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| title_fullStr | Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| title_full_unstemmed | Lectures on measure and integration by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| title_short | Lectures on measure and integration |
| title_sort | lectures on measure and integration by harold widom notes by david drasin and anthony j tromba |
| title_sub | by Harold Widom. Notes by David Drasin and Anthony J.Tromba |
| topic | Integrals, Generalized Measure Theory Maßtheorie (DE-588)4074626-4 gnd Integrationstheorie (DE-588)4138369-2 gnd |
| topic_facet | Integrals, Generalized Measure Theory Maßtheorie Integrationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001986942&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021856926 |
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