Metrics, Norms and Integrals: An Introduction to Contemporary Analysis

Metrics, Norms and Integrals: An Introduction to Contemporary Analysis


By (author) Jerry J. Koliha

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  • Publisher: World Scientific Publishing Co Pte Ltd
  • Format: Paperback | 412 pages
  • Dimensions: 152mm x 228mm x 24mm | 621g
  • Publication date: 13 November 2008
  • Publication City/Country: Singapore
  • ISBN 10: 9812836578
  • ISBN 13: 9789812836571
  • Illustrations note: black & white illustrations, figures
  • Sales rank: 527,833

Product description

"Metrics, Norms and Integrals" is a textbook on contemporary analysis based on the author's lectures given at the University of Melbourne for over two decades. It covers three main topics: metric and topological spaces, functional analysis, and the theory of the Lebesgue integral on measure spaces. This self-contained text contains a number of original presentations, including an early introduction of pseudometric spaces to motivate general topologies, an innovative introduction to the Lebesgue integral, and a discussion on the use of the Newton integral. It is thus a valuable book to inform and stimulate both undergraduate and graduate students.

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Table of contents

Metrics and Topologies: Metric Spaces; Convergence and Completeness; Continuity; Topological Spaces; Compactness; Connectedness; Linear Analysis: Normed Spaces; Inner Product Spaces; Linear Operators and Functionals; Self-Adjoint Compact Operators; Functional Analysis; Integration: Measure Spaces; Abstract Lebesgue Integral; Integral on the Real Line; Construction of Measures; Product Measures; Lebesgue Spaces.