Description
CAMBRIDGE UNIVERSITY PRESS Measures, Integrals And Martingales by Rene L. Schilling
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 Jacobis transformation theorem the RadonNikodym theorem differentiation of measures and HardyLittlewood maximal functions. In this second edition readers will find newly added chapters on Hausdorff measures Fourier analysis vague convergence and classical proofs of RadonNikodym 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 selfstudy. Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge. Full solutions to all exercises are available on the authors webpage at www.motapa.de.