Opuscula Math. 31, no. 2 (2011), 159-172
Convolution algebras for topological groupoids with locally compact fibres
Abstract. The aim of this paper is to introduce various convolution algebras associated with a topological groupoid with locally compact fibres. Instead of working with continuous functions on \(G\), we consider functions having a uniformly continuity property on fibres. We assume that the groupoid is endowed with a system of measures (supported on its fibres) subject to the "left invariance" condition in the groupoid sense.
Keywords: convolution algebra, groupoid, uniform continuity, Haar system.
Mathematics Subject Classification: 22A22, 43A10.