On the Continuity of Haar Measure on Topological Groupoids
نویسنده
چکیده
It is shown that continuity of a family of invariant (Haar) measures on a topological groupoid G is equivalent to the continuity of the implied convolution product f * g for all pairs of functions / and g. An example is given of a groupoid which admits no (continuous) Haar measure. It results, therefore, that the usual C*-algebra associated with a Haar measure on G cannot, in general, be constructed. Some remarks are included concerning the construction of Haar measures on the holonomy groupoid of a foliated manifold.
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