Description

Book Synopsis
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.

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.

Metrics, Norms And Integrals: An Introduction To Contemporary Analysis

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    A Paperback by Jerry J Koliha

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      View other formats and editions of Metrics, Norms And Integrals: An Introduction To Contemporary Analysis by Jerry J Koliha

      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 13/11/2008
      ISBN13: 9789812836571, 978-9812836571
      ISBN10: 9812836578

      Description

      Book Synopsis
      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.

      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.

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