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Decomposition of probability measures on locally compact abelian groups

  • R. G. Laha
  • V. K. Rohatgi
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)

Abstract

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.

Keywords

Probability Measure Steklov Institute Gaussian Measure Borel Subset Compact ABELIAN Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • R. G. Laha
    • 1
  • V. K. Rohatgi
    • 1
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling Green

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