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Probability Measures on Locally Compact Groups

  • Book
  • © 1977

Overview

Authors:
  1. Herbert Heyer

    1. Mathematisches Institut, Universität Tübingen, Tübingen 1, Germany

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Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (MATHE2, volume 94)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-X
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  2. Introduction

    • Herbert Heyer
    Pages 1-4

  3. Preliminaries

    • Herbert Heyer
    Pages 5-16

  4. Harmonic Analysis of Almost Periodic Locally Compact Groups

    • Herbert Heyer
    Pages 17-86

  5. Convergence of Convolution Sequences of Probability Measures

    • Herbert Heyer
    Pages 87-162

  6. Embedding of Infinitely Divisible Probability Measures

    • Herbert Heyer
    Pages 163-248

  7. Canonical Representations of Convolution Semigroups

    • Herbert Heyer
    Pages 249-335

  8. The Central Limit Problem in the Abelian Case

    • Herbert Heyer
    Pages 336-407

  9. The Central Limit Problem in the General Case

    • Herbert Heyer
    Pages 408-503

  10. Back Matter

    Pages 504-534
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Keywords

About this book

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.

Authors and Affiliations

  • Mathematisches Institut, Universität Tübingen, Tübingen 1, Germany

    Herbert Heyer

Bibliographic Information

  • Book Title: Probability Measures on Locally Compact Groups

  • Authors: Herbert Heyer

  • Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge

  • DOI: https://doi.org/10.1007/978-3-642-66706-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1977

  • Softcover ISBN: 978-3-642-66708-4Published: 14 December 2011

  • eBook ISBN: 978-3-642-66706-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: X, 532

  • Topics: Applications of Mathematics

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