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Summary: NOTES ON MEASURE AND INTEGRATION
IN LOCALLY COMPACT SPACES
William Arveson
Department of Mathematics
University of California
Berkeley, CA 94720 USA
25 March 1996
Abstract. This is a set of lecture notes which present an economical development
of measure theory and integration in locally compact Hausdorff spaces. We have tried
to illuminate the more difficult parts of the subject. The Riesz-Markov theorem is
established in a form convenient for applications in modern analysis, including Haar
measure on locally compact groups or weights on C-algebras...though applications
are not taken up here. The reader should have some knowledge of basic measure
theory, through outer measures and Carath´eodory's extension theorem.
Contents
Introduction
1. The trouble with Borel sets
2. How to construct Radon measures
3. Measures and linear functionals
4. Baire meets Borel
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