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Convolution algebras for topological groupoids with locally compact fibres

Buneci M. R.

Opuscula Mathematica

2011

Vol. 31, no. 2

159-172

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.