Measure and Integration Theory
Transl. by Burckel, Robert B.
Series:De Gruyter Studies in Mathematics 26
Aims and Scope
This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem.
The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory.
The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.
"It is a pleasure to see Heinz Bauer's famous monograph Maß- und Intergrationstheorie [...] published in English. [...] The translation by Robert B. Burckel is careful and close to the German original. He has replaced references to German textbooks by references to English textbooks, and he has also added several interesting exercises, comments, and references. the typographical appearance of the book is excellent."
Klaus D. Schmidt in: Zentralblatt Math, 10/2000
"Like the German original, the present textbook is a very readable and concise introduction to measure theory and integration.[...] In any case, it definitely is a valuable resource for both students and teachers."
G. Teschl in: Internationale Mathematische Nachrichten, Wien, 189/2002