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Englisch
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Beschreibung
A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.
A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.
Über den Autor
René L. Schilling is a Professor of Mathematics at Technische Universität, Dresden. His main research area is stochastic analysis and stochastic processes.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: | 2019 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
ISBN-13: | 9781316620243 |
ISBN-10: | 1316620247 |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: | Schilling, René L. |
Hersteller: | Cambridge University Press |
Maße: | 246 x 189 x 27 mm |
Von/Mit: | René L. Schilling |
Erscheinungsdatum: | 01.03.2019 |
Gewicht: | 0,95 kg |
Über den Autor
René L. Schilling is a Professor of Mathematics at Technische Universität, Dresden. His main research area is stochastic analysis and stochastic processes.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: | 2019 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
ISBN-13: | 9781316620243 |
ISBN-10: | 1316620247 |
Sprache: | Englisch |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: | Schilling, René L. |
Hersteller: | Cambridge University Press |
Maße: | 246 x 189 x 27 mm |
Von/Mit: | René L. Schilling |
Erscheinungsdatum: | 01.03.2019 |
Gewicht: | 0,95 kg |
Warnhinweis