Measures, Integrals and Martingales van Rene L. Schilling is een Engelstalig gedrukt boek. Deze titel is geschikt voor studenten in het hoger onderwijs en professionals.
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 Rene Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).
Measure and integration are key topics in many areas of mathematics, including analysis, probability, mathematical physics and finance. This book offers a concise yet elementary introduction in which the theory is quickly and simply developed. Few prerequisites are required, making the text suitable for undergraduate lecture courses or self-study.
A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.
Inhoudelijk sluit dit boek aan bij onderwerpen als Probability and statistics, Stochastics, MATHEMATICS / Probability & Statistics / General.