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Measures, Integrals and Martingales Vital Source e-bog
René L. Schilling
(2017)
Cambridge University Press
451,00 kr.
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Søgbar e-bog
Measures, Integrals and Martingales Vital Source e-bog
René L. Schilling
(2017)
Cambridge University Press
587,00 kr.
Leveres umiddelbart efter køb
Measures, Integrals and Martingales
René L. Schilling
(2017)
Sprog: Engelsk
Cambridge University Press
559,00 kr.
1 stk på lager
Hvor er varen på lager?Detaljer om varen
- 2. Udgave
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: Cambridge University Press (April 2017)
- ISBN: 9781108161275
A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author's webpage at www.motapa.de. This book forms a sister volume to René Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).
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Detaljer om varen
- 2. Udgave
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Cambridge University Press (April 2017)
- ISBN: 9781108162395
A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author's webpage at www.motapa.de. This book forms a sister volume to René Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).
Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: 2 sider kan printes ad gangen
Copy: højest 2 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- 2. Udgave
- Paperback: 490 sider
- Udgiver: Cambridge University Press (April 2017)
- ISBN: 9781316620243
A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance. In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further. Other topics are also covered such as Jacobi's transformation theorem, the Radon-Nikodym theorem, differentiation of measures and Hardy-Littlewood maximal functions. In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon-Nikodym and Riesz representation theorems. All proofs are carefully worked out to ensure full understanding of the material and its background. Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the author's webpage at www.motapa.de.
List of symbols; Prelude; Dependence chart;
1. Prologue;
2. The pleasures of counting;
3. -algebras;
4. Measures;
5. Uniqueness of measures;
6. Existence of measures;
7. Measurable mappings;
8. Measurable functions;
9. Integration of positive functions;
10. Integrals of measurable functions;
11. Null sets and the 'almost everywhere';
12. Convergence theorems and their applications;
13. The function spaces Lp;
14. Product measures and Fubini's theorem;
15. Integrals with respect to image measures;
16. Jacobi's transformation theorem;
17. Dense and determining sets;
18. Hausdorff measure;
19. The Fourier transform;
20. The Radon-Nikodym theorem;
21. Riesz representation theorems;
22. Uniform integrability and Vitali's convergence theorem;
23. Martingales;
24. Martingale convergence theorems;
25. Martingales in action;
26. Abstract Hilbert spaces;
27. Conditional expectations;
28. Orthonormal systems and their convergence behaviour; Appendix A. Lim inf and lim sup; Appendix B. Some facts from topology; Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index. Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index. Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index. Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index.
1. Prologue;
2. The pleasures of counting;
3. -algebras;
4. Measures;
5. Uniqueness of measures;
6. Existence of measures;
7. Measurable mappings;
8. Measurable functions;
9. Integration of positive functions;
10. Integrals of measurable functions;
11. Null sets and the 'almost everywhere';
12. Convergence theorems and their applications;
13. The function spaces Lp;
14. Product measures and Fubini's theorem;
15. Integrals with respect to image measures;
16. Jacobi's transformation theorem;
17. Dense and determining sets;
18. Hausdorff measure;
19. The Fourier transform;
20. The Radon-Nikodym theorem;
21. Riesz representation theorems;
22. Uniform integrability and Vitali's convergence theorem;
23. Martingales;
24. Martingale convergence theorems;
25. Martingales in action;
26. Abstract Hilbert spaces;
27. Conditional expectations;
28. Orthonormal systems and their convergence behaviour; Appendix A. Lim inf and lim sup; Appendix B. Some facts from topology; Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index. Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index. Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index. Appendix C. The volume of a parallelepiped; Appendix D. The integral of complex valued functions; Appendix E. Measurability of the continuity points of a function; Appendix F. Vitali's covering theorem; Appendix G. Non-measurable sets; Appendix H. Regularity of measures; Appendix I. A summary of the Riemann integral; References; Name and subject index.
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