Decomposition of probability measures on locally compact abelian groups
Let G be a locally compact, separable, Abelian metric group. Let B be the σ-field of Borel subsets of G and let P be the class of all probability measures on B. Let I ⊂ P be the class of all infinitely divisible probability measures. Let I0 ⊂ I be the class of all measures which have no indecomposable or idempotent factors. One of the fundamental problems in analytic probability theory is to obtain a precise description of the class I0. This problem is very difficult and has net yet been solved even for the case G = ℝ. It is therefore important to determine conditions under which a measure P∈I does or does not belong to I0. This paper surveys the recent work on this subject.
KeywordsProbability Measure Steklov Institute Gaussian Measure Borel Subset Compact ABELIAN Group
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