Bøger af John L. Kelley

This is a systematic exposition of the basic part of the theory of mea- sure and integration. The book is intended to be a usable text for students with no previous knowledge of measure theory or Lebesgue integration, but it is also intended to include the results most com- monly used in functional analysis. Our two intentions are some what conflicting, and we have attempted a resolution as follows. The main body of the text requires only a first course in analysis as background. It is a study of abstract measures and integrals, and comprises a reasonably complete account of Borel measures and in- tegration for R Each chapter is generally followed by one or more supplements. These, comprising over a third of the book, require some- what more mathematical background and maturity than the body of the text (in particular, some knowledge of general topology is assumed) and the presentation is a little more brisk and informal. The material presented includes the theory of Borel measures and integration for ~n, the general theory of integration for locally compact Hausdorff spaces, and the first dozen results about invariant measures for groups. Most of the results expounded here are conventional in general character, if not in detail, but the methods are less so. The following brief overview may clarify this assertion.

The clarity of the author's thought and the carefulness of his exposition make reading this book a pleasure, noted the Bulletin of the American Mathematical Society upon the 1955 publication of John L. Kelley's General Topology. This comprehensive treatment for beginning graduate-level students immediately found a significant audience, and it remains a highly worthwhile and relevant book for students of topology and for professionals in many areas. A systematic exposition of the part of general topology that has proven useful in several branches of mathematics, this volume is especially intended as background for modern analysis. An extensive preliminary chapter presents mathematical foundations for the main text. Subsequent chapters explore topological spaces, the Moore-Smith convergence, product and quotient spaces, embedding and metrization, and compact, uniform, and function spaces. Each chapter concludes with an abundance of problems, which form integral parts of the discussion as well as reinforcements and counter examples that mark the boundaries of possible theorems. The book concludes with an extensive index that provides supplementary material on elementary set theory.Dover (2017) republication of the edition published by the Van Nostrand Reinhold Company, New York, 1955.www.doverpublications.com

Aimed at graduate math students, this classic work is a systematic exposition of general topology and is intended to be a reference and a text. As a reference, it offers a reasonably complete coverage of the area, resulting in a more extended treatment than normally given in a course.

The material presented includes the theory of Borel measures and integration for ~n, the general theory of integration for locally compact Hausdorff spaces, and the first dozen results about invariant measures for groups.