Measures, Integrals and Martingales (Paperback)

Measures, Integrals and Martingales By René L. Schilling Cover Image
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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 This book forms a sister volume to Ren Schilling's other book Counterexamples in Measure and Integration (

Product Details
ISBN: 9781316620243
ISBN-10: 1316620247
Publisher: Cambridge University Press
Publication Date: April 3rd, 2017
Pages: 490
Language: English