Vol. 60, No. 2, 1975

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On the groups of units in semigroups of probability measures

John Yuan

Vol. 60 (1975), No. 2, 303–312
Abstract

We generalize Pym’s decomposition w = μE wH μF of idempotent probability measures to the decomposition μE ∗ℋ(wH) μF of the maximal groups of units in semigroup of probability measures on a compact semitopological semigroup. We also prove that (w)(wH)N(H)∕H algebraically and topologically. With these characterizations, we verify Rosenblatt’s necessary and sufficient condition for the convergence of a convolution sequence (νn)n1 of a probability measure ν on a compact topological semigroup.

Mathematical Subject Classification 2000
Primary: 43A05
Secondary: 60B15
Milestones
Received: 9 August 1974
Revised: 20 March 1975
Published: 1 October 1975
Authors
John Yuan