E-Book, Englisch, Band Volume 95, 446 Seiten, Web PDF
Dinculeanu / Sneddon / Stark Vector Measures
1. Auflage 2014
ISBN: 978-1-4832-2265-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band Volume 95, 446 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4832-2265-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
International Series of Monographs in Pure and Applied Mathematics, Volume 95: Vector Measures focuses on the study of measures with values in a Banach space, including positive measures with finite or infinite values. This book is organized into three chapters. Chapter I covers classes of sets, set functions, variation and semi-variation of set functions, and extension of set functions from a certain class to a wider one. The integration of vector functions with respect to vector measures is reviewed in Chapter II. In Chapter III, the regular measures on a locally compact space and integral representation of the dominated operations on the space of continuous functions with compact carrier are described. This volume is intended for specialists, researchers, and students interested in vector measures.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Vector Measures;4
3;Copyright Page;5
4;Table of Contents;8
5;PREFACE;6
6;Chapter I. Vector measures;12
6.1;§ 1. Classes of sets;12
6.2;§ 2. Set functions;25
6.3;§ 3. Variation of set functions;43
6.4;§ 4. Semi-variation of set functions;61
6.5;§ 5. Extension of set functions;68
7;Chapter II. Integration;93
7.1;§ 6. Measurable functions;93
7.2;§ 7. Integration of step functions;117
7.3;§ 8. Integrable functions;130
7.4;§ 9. The spaces M8E and L8E;150
7.5;§ 10. Measures defined by densities;174
7.6;§ 11. The lifting property of the space L8;210
7.7;§ 12. The spaces LPE;228
7.8;§ 13. Linear operations on LPE;252
8;Chapter III. Regular measures;298
8.1;§ 14. Borei sets. Borei measures;298
8.2;§ 15. Regular measures;312
8.3;§ 16. Construction and extension of regular measures;350
8.4;§ 17. Stieltjes measures on the real line;367
8.5;§ 18. Reduction of the integration on abstract spaces to the integration on locally compact spaces;379
8.6;§ 19. Integral representation of line ar operations on KE(T);385
8.7;§ 20. Disintegration of measures;413
9;Notes and remarks;424
10;Bibliography;428
11;Index of notations;438
12;Index;440
13;Other titles published in this series;444
