Probability Measures on Locally Compact Groups

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 Levy 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 Levy-Khintchine Formula for Almost Periodic Groups.- 4.4 The Canonical Representation of Almost Positive Functionals.- 4.5 The Levy-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.