Probability Measures on Locally Compact Groups

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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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.

• Finite
• Lokal kompakte Gruppe
• Measure theory
• Probability
• Wahrscheinlichkeitsmass
• algebra
• topological groups

• Mathematisches Institut, Universität Tübingen, Tübingen 1, Germany

  Herbert Heyer