Continuity of convolution and SIN groups

Abstract

Let the measure algebra of a topological group be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if the group has the SIN property.

8 pages. New in version 3: Updated title, Theorem 4.4 and its corollaries

Cited by in corpus (2)

• On Følner sets in topological groups
• On amenability and groups of measurable maps