Research Catalog

Title

Probability measures on locally compact groups / Herbert Heyer.

Author

Heyer, Herbert

Publication

Berlin ; New York : Springer-Verlag, 1977.

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Details

Series Statement

Ergebnisse der Mathematik und ihrer Grenzgebiete ; Bd. 94

Uniform Title

Ergebnisse der Mathematik und ihrer Grenzgebiete n.F., Heft 94.

Subject

• Probabilities
• Measure theory
• Locally compact groups

Note

• Includes index.

Bibliography (note)

• Bibliography: p. 504-522.

Contents

Preliminaries. Almost Periodic Locally Compact Groups -- References and Comments -- I. Harmonic Analysis of Almost Periodic Locally Compact Groups -- 1.1 Measures on a Locally Compact Space -- 1.2 Convolution of Measures on a Locally Compact Group -- 1.3 Fourier Transforms of Bounded Measures -- 1.4 The Theorems of Lévy and Bochner -- 1.5 Convolution Semigroups and Negative-Definite Forms -- References and Comments -- II. Convergence of Convolution Sequences of Probability Measures -- 2.1 Convolution Powers on a Compact Group -- 2.2 Equivalence of Types of Convergence -- 2.3 The Normed Convergence Property -- 2.4 Convergence in Variance -- 2.5 Asymptotic Equidistribution -- 2.6 Shifting Iterated Convolutions -- References and Comments -- III. Embedding of Infinitely Divisible Probability Measures -- 3.1 Root Compact Groups -- 3.2 Poisson Measures and Their Characterizations -- 3.3 Submonogeneous Embedding of Infinitely Divisible Measures -- 3.4 Existence of One-Parameter Semigroups -- 3.5 The General Continuous Embedding -- 3.6 Injective Submonogeneous Embeddings -- References and Comments -- IV. Canonical Representations of Convolution Semigroups -- 4.1 Positive Semigroups and Their Generating Functionals -- 4.2 Hunt's Representation Theorem -- 4.3 The Lévy-Khintchine Formula for Almost Periodic Groups -- 4.4 The Canonical Representation of Almost Positive Functionals -- 4.5 The Lévy-Khintchine Formula for General Locally Compact Groups -- 4.6 Convolution Hemigroups. Generation and Representation -- References and Comments -- V. The Central Limit Problem in the Abelian Case -- 5.1 Convergence of Infinitesimal Systems -- 5.2 Gauss Measures in the Sense of Parthasarathy -- 5.3 Gauss Measures in the Sense of Bernstein -- 5.4 Convergence to Gauss Measures -- 5.5 Symmetric Gauss Semigroups -- 5.6 Additive Processes and Their Decomposition -- References and Comments -- VI. The Central Limit Problem in the General Case -- 6.1 Poisson Embedding and Approximation -- 6.2 Gauss Measures and Their Characterizations -- 6.3 Absolute Continuity and Diffusion of Gauss Semigroups -- 6.4 Central Gauss Semigroups -- 6.5 Convergence of Triangular Systems of Probability Measures -- 6.6 Central Limit Theorems for Totally Disconnected Groups -- References and Comments -- List of Symbols.

ISBN

0387083324

LCCN

^^^77024147^

OCLC

• 3089570
• SCSB-10045609

Owning Institutions

Harvard Library