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Zbl 0593.28015
Seda, Anthony Karel
On the continuity of Haar measure on topological groupoids. (English)
[J] Proc. Am. Math. Soc. 96, 115-120 (1986). ISSN 0002-9939; ISSN 1088-6826/e

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 f and g. An example is given of a groupoid which admits no (continuous) Haar measure. It results, therefore, that the usual $C\sp*$-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.

MSC 2000:: *28C10 Set functions and measures on topological groups
46L99 Selfadjoint operator algebras

Keywords: continuity of a family of invariant (Haar) measures on a; topological groupoid; continuity of the implied convolution product; $C\sp*$-algebra associated with a Haar measure; holonomy groupoid of a foliated manifold; continuity of a family of invariant (Haar) measures on a topological groupoid

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