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Probability Measures on Locally Compact Groups

  • Herbert Heyer

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 94)

Table of contents

  1. Front Matter
    Pages I-X
  2. Herbert Heyer
    Pages 1-4
  3. Herbert Heyer
    Pages 5-16
  4. Herbert Heyer
    Pages 336-407
  5. Herbert Heyer
    Pages 408-503
  6. Back Matter
    Pages 504-534

About this book

Introduction

Probability measures on algebraic-topological structures such as topological semi­ groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob­ ability measures on locally compact groups. At the same time we stress the non­ Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Keywords

Finite Lokal kompakte Gruppe Measure theory Probability Wahrscheinlichkeitsmass algebra topological groups

Authors and affiliations

  • Herbert Heyer
    • 1
  1. 1.Mathematisches InstitutUniversität TübingenTübingen 1Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-66706-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1977
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-66708-4
  • Online ISBN 978-3-642-66706-0
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site