Fields Institute Monographs

Uniform Spaces and Measures

Authors: Pachl, Jan

  • ​Presents a self-contained development of selected topics in the theory of uniform spaces using pseudometrics rather than the more common approach via entourages
  • Contains exercises and research problems and can be used as supplementary text in graduate and advanced undergraduate courses
  • Details the history of core concepts and links to key references to help the reader understand connections to related areas and explore other sources​
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  • ISBN 978-1-4614-5058-0
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Hardcover $129.00
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valid through November 5, 2017
  • ISBN 978-1-4614-5057-3
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Softcover $129.00
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  • ISBN 978-1-4899-9258-1
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About this book

​This book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain 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 abstract and 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. The book is 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 presents diverse results from many sources organized in a logical whole, and includes several new results. The book is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis. The text contains a number of exercises with solution hints, and four problems with suggestions for further research.​

Reviews

From the reviews:

“The material of this book is arranged into one preliminary section for auxiliary prerequisites plus three parts. … Each of these parts is divided into chapters, every one of which ends with several complementary and historical notes that clearly help one to gain a better understanding of the material being covered. … this is a book which every researcher interested in measure theory and its applications must consider for library acquisition and personal use.” (Jesús Ferrer, Mathematical Reviews, August, 2013)

Table of contents (13 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-5058-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4614-5057-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
valid through November 5, 2017
  • ISBN 978-1-4899-9258-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Uniform Spaces and Measures
Authors
Series Title
Fields Institute Monographs
Series Volume
30
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-5058-0
DOI
10.1007/978-1-4614-5058-0
Hardcover ISBN
978-1-4614-5057-3
Softcover ISBN
978-1-4899-9258-1
Series ISSN
1069-5273
Edition Number
1
Number of Pages
X, 210
Topics