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Collapsible probability measures and concentration functions on Lie groups

Published online by Cambridge University Press:  01 July 1997

S. G. DANI  and
RIDDHI SHAH
S. G. DANI
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Bombay 400 005, India
RIDDHI SHAH
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Bombay 400 005, India
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Abstract

Given a locally compact group G and a probability measure μ on G it is of interest to know, in various situations, whether there exist divergent sequences {gn} such that {gn μg−1n is relatively compact (see for example [DM3] and [DS]); this phenomenon may be viewed as ‘collapsing’ of the measure. It is the purpose of this note to prove Theorem 1 below and give certain applications to the asymptotic behaviour of concentration functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 1 , July 1997 , pp. 105 - 113
Copyright
Cambridge Philosophical Society 1997

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