Opuscula Math. 31, no. 2 (2011), 159-172
http://dx.doi.org/10.7494/OpMath.2011.31.2.159

Opuscula Mathematica

# Convolution algebras for topological groupoids with locally compact fibres

Mădălina Roxana Buneci

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.

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