Metrics, Norms and Integrals

Metrics, Norms and Integrals : An Introduction to Contemporary Analysis

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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.show more

Product details

  • Paperback | 428 pages
  • 152 x 228 x 24mm | 621.42g
  • World Scientific Publishing Co Pte Ltd
  • Singapore, Singapore
  • English
  • black & white illustrations, figures
  • 9812836578
  • 9789812836571
  • 665,908

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.show more