Uniform Spaces and Measures

  • Jan┬áPachl

Part of the Fields Institute Monographs book series (FIM, volume 30)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Uniform Spaces

    1. Front Matter
      Pages 17-17
    2. Jan Pachl
      Pages 1-16
    3. Jan Pachl
      Pages 19-28
    4. Jan Pachl
      Pages 29-39
    5. Jan Pachl
      Pages 41-51
  3. Uniform Measures

    1. Front Matter
      Pages 61-61
    2. Jan Pachl
      Pages 63-79
    3. Jan Pachl
      Pages 81-98
    4. Jan Pachl
      Pages 99-116
    5. Jan Pachl
      Pages 117-127
    6. Jan Pachl
      Pages 129-147
  4. Topics From Farther Afield

    1. Front Matter
      Pages 149-149
    2. Jan Pachl
      Pages 151-169
    3. Jan Pachl
      Pages 179-185
  5. Back Matter
    Pages 187-209

About this book

Introduction

Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations.

Uniform measures are functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups.

This book can serve as a reference for the theory of uniform measures. It includes a self-contained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes several new results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and contains a number of exercises with hints to solutions as well as several open problems with suggestions for further research.

Keywords

abstract harmonic analysis semitopological semigroups topologies on spaces of measures uniform measures

Authors and affiliations

  • Jan┬áPachl
    • 1
  1. 1.The Fields Institute for Research in MatTorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-5058-0
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-5057-3
  • Online ISBN 978-1-4614-5058-0
  • Series Print ISSN 1069-5273
  • Series Online ISSN 2194-3079
  • About this book