Uniform spaces and measures Jan Pachl

Format:

Book

Author/Creator:

Pachl, Jan

Series:

Fields Institute monographs ; 1069-5273 30

Fields Institute Monographs 1069-5273 30

Language:

English

Subjects (All):

Measure theory.

Fourier analysis.

Functional analysis.

Functions of complex variables.

Mathematics.

Fourier Analysis.

mathematics.

applied mathematics.

Medical Subjects:

Mathematics.

Fourier Analysis.

Physical Description:

1 online resource

Place of Publication:

New York Springer Toronto, ON Fields Institute for Research in Mathematical Sciences ©2013

System Details:

text file

PDF

Summary:

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now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations.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

Contents:

Prerequisites

1. Uniformities and Topologies

2. Induced Uniform Structures

3. Uniform Structures on Semigroups

4. Some Notable Classes of Uniform Spaces

5. Measures on Complete Metric Spaces

6. Uniform Measures

7. Uniform Measures as Measures

8. Instances of Uniform Measures

9. Direct Product and Convolution

10. Free Uniform Measures

11. Approximation of Probability Distributions

12. Measurable Functionals

Hints to Excercises

References

Notation Index

Author Index

Subject Index

Other Format:

Print version:

ISBN:

9781461450580

1461450586

OCLC:

1111042686

Access Restriction:

Restricted for use by site license