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Measures, integrals and martingales. (English) Zbl 1084.28001
Cambridge: Cambridge University Press (ISBN 0-521-61525-9/pbk; 0-521-85015-0/hbk). x, 381 p. £ 24.95, $ 50.00/pbk; £ 50.00, $ 90.00/hbk (2005).

The present book is an elementary but thorough introduction to a wide variety of first year graduate level topics in analysis including the Lebesgue integral, abstract measure theory, and associated theorems such as the Fubini-Tonelli theorem, and the Jacobi transformation theorem for integrals. The topics also lay the foundation for advanced probability theory by introducing filtered measure spaces, associated martingales, and convergence theorems with application to the Raydon-Nikodým theorem.

The author includes an introduction to many other topics that might be found in a standard functional analysis course such as Hilbert spaces, the uniform boundedness principle, and orthogonal systems.

This book should be accessible to anyone with a strong undergraduate background in calculus, linear algebra, and real analysis.

MSC:
28-01Textbooks (measure and integration)
28A60Measures on Boolean rings, measure algebras
28A33Spaces of measures, convergence of measures
28A35Measures and integrals in product spaces