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)


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.


Probability Measure Steklov Institute Gaussian Measure Borel Subset Compact ABELIAN Group 
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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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