A BERNSTEIN PROPERTY OF MEASURES ON GROUPS AND
Abstract: In this paper we consider a Bernstein property of probability measures on groups
introduced by Neuenschwander. We discuss this property for discrete groups, compact
groups, nilpotent groups and some solvable groups. In all these cases we show that a measure
having the Bernstein-Neuenschwander property must be concentrated on an Abelian
subgroup. We conclude with an application of this result to the Gaussian measures on
non-compact symmetric spaces.
1991 AMS Mathematics Subject Classification: Primary 43A05, 62H05; Secondary
Key words and phrases: Bernstein property of measures, probability measures on
non-commutative groups, Gaussian measures on symmetric spaces.