Measures, Integrals and Martingales
Publisher: Cambridge University Press
Published: January 16, 2006
Language: eng
Format: Paperback
Number of pages: 381
ISBN-13: 9780521615259
Subjects: Calculus & mathematical analysis; Science/Mathematics; Mathematics; Differential Equations; Mathematics / Differential Equations; Calculus
First sentence: The theme of this book is the problem of how to assign a size, a content, a probability, etc. to certain sets.
Description: This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability theory. The basic theory - measures, integrals, convergence theorems, Lp-spaces and multiple integrals - is explored in the first part of the book. The second part then uses the notion of martingales to develop the theory further, covering topics such as Jacobi's generalized transformation Theorem, the Radon-Nikodym theorem, Hardy-Littlewood maximal functions or general Fourier series. Undergraduate calculus and an introductory course on rigorous analysis are the only essential prerequisites, making this text suitable for both lecture courses and for self-study. Numerous illustrations and exercises are included and these are not merely drill problems but are there to consolidate what has already been learnt and to discover variants, sideways and extensions to the main material. Hints and solutions can be found on the author's website, which can be reached from www.cambridge.org/9780521615259.