{"product_id":"measures-integrals-and-martingales-paperback-9781316620243","title":"Measures, Integrals and Martingales (Paperback \/ softback) 9781316620243","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eMeasures, Integrals and Martingales\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eRené L. Schilling (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781316620243, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 3 April 2017\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e490 pages, 40 b\/w illus.  420 exercises\u003cbr\u003e24.7 x 17.4 x 2.2 cm, 0.97 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This book is an admirable counterpart, both to the first author's well-known text Measures, Integrals and Martingales (CUP, 2005\/2017), and to the books on counter-examples in analysis (Gelbaum and Olmsted), topology (Steen and Seebach) and probability (Stoyanov). To paraphrase, the authors' preface: in a good theory, it is valuable and instructive to probe the limits of what can be said by investigating what cannot be said. The task is thus well-conceived, and the execution is up to the standards one would expect from the books of the first author and of their papers. I recommend it warmly.' Professor N. H. Bingham, Imperial College London\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eA 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).\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eList of symbols\u003cbr\u003e Prelude\u003cbr\u003e Dependence chart\u003cbr\u003e 1. Prologue\u003cbr\u003e 2. The pleasures of counting\u003cbr\u003e 3. ?-algebras\u003cbr\u003e 4. Measures\u003cbr\u003e 5. Uniqueness of measures\u003cbr\u003e 6. Existence of measures\u003cbr\u003e 7. Measurable mappings\u003cbr\u003e 8. Measurable functions\u003cbr\u003e 9. Integration of positive functions\u003cbr\u003e 10. Integrals of measurable functions\u003cbr\u003e 11. Null sets and the 'almost everywhere'\u003cbr\u003e 12. Convergence theorems and their applications\u003cbr\u003e 13. The function spaces Lp\u003cbr\u003e 14. Product measures and Fubini's theorem\u003cbr\u003e 15. Integrals with respect to image measures\u003cbr\u003e 16. Jacobi's transformation theorem\u003cbr\u003e 17. Dense and determining sets\u003cbr\u003e 18. Hausdorff measure\u003cbr\u003e 19. The Fourier transform\u003cbr\u003e 20. The Radon–Nikodym theorem\u003cbr\u003e 21. Riesz representation theorems\u003cbr\u003e 22. Uniform integrability and Vitali's convergence theorem\u003cbr\u003e 23. Martingales\u003cbr\u003e 24. Martingale convergence theorems\u003cbr\u003e 25. Martingales in action\u003cbr\u003e 26. Abstract Hilbert spaces\u003cbr\u003e 27. Conditional expectations\u003cbr\u003e 28. Orthonormal systems and their convergence behaviour\u003cbr\u003e Appendix A. Lim inf and lim sup\u003cbr\u003e Appendix B. Some facts from topology\u003cbr\u003e Appendix C. The volume of a parallelepiped\u003cbr\u003e Appendix D. The integral of complex valued functions\u003cbr\u003e Appendix E. Measurability of the continuity points of a function\u003cbr\u003e Appendix F. Vitali's covering theorem\u003cbr\u003e Appendix G. Non-measurable sets\u003cbr\u003e Appendix H. Regularity of measures\u003cbr\u003e Appendix I. A summary of the Riemann integral\u003cbr\u003e References\u003cbr\u003e Name and subject index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Stochastics [\u003ca title=\"See our other books on Stochastics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Stochastics%20%5BPBWL%5D%22\"\u003ePBWL\u003c\/a\u003e], Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46000570794264,"sku":"9781316620243","price":40.69,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781316620243i_d6075927-5cdd-4777-9e58-0ffdfdd148ec.jpg?v=1696683118","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/measures-integrals-and-martingales-paperback-9781316620243","provider":"Freshly Printed Books","version":"1.0","type":"link"}