On the factor sets of measures and local tightness of convolution semigroups over Lie groups |
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Authors: | S G Dani M McCrudden |
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Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, 40005 Bombay, India;(2) Department of Mathematics, University of Manchester, M13 9PL Manchester, England |
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Abstract: | It is shown that for a large class of Lie groups (called weakly algebraic groups) including all connected semisimple Lie groups the following holds: for any probability measure on the Lie group the set of all two-sided convolution factors is compact if and only if the centralizer of the support of inG is compact. This is applied to prove that for any connected Lie groupG, any homomorphism of any real directed (submonogeneous) semigroup into the topological semigroup of all probability measures onG is locally tight. |
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Keywords: | Lie group probability measures convolution semigroups local tightness |
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