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. A very clear exposition which will take the 'fear' out of measure and integration theory Contains clearly structured proofs and numerous exercises designed to deepen understanding of the material Full solutions to all problems are available online, making the text useful for self-study
- ISBN: 9781316620243
- Editorial: CAMBRIDGE UNIVERSITY PRESS
- Encuadernacion: Rústica
- Fecha Publicación: 01/04/2017
- Nº Volúmenes: 1
- Idioma: