Mathematical Proceedings of the Cambridge Philosophical Society


Research Article

Collapsible probability measures and concentration functions on Lie groups


S. G. DANI a1 and RIDDHI SHAH a1
a1 School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Bombay 400 005, India

Abstract

Given a locally compact group G and a probability measure [mu] on G it is of interest to know, in various situations, whether there exist divergent sequences {gn} such that {gn [mu]g[minus sign]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.

(Received October 2 1995)
(Revised February 6 1996)