Geodesic
Continuity of Convolution and SIN Groups
Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 845-854

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Let the measure algebra of a topological group $G$ be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly continuous if and only if $G$ has the $\text{SIN}$ property. On the larger space $\text{LUC}{{(G)}^{*}}$ , which includes the measure algebra, convolution is also jointly continuous if and only if the group has the $\text{SIN}$ property, but not separately continuous for many non-SIN groups.
DOI : 10.4153/CMB-2017-002-9
Mots-clés : 43A10, 22A10, topological group, SIN property, measure algebra, convolution 
Pachl, Jan; Steprans, Juris. Continuity of Convolution and SIN Groups. Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 845-854. doi: 10.4153/CMB-2017-002-9
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     title = {Continuity of {Convolution} and {SIN} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {845--854},
     year = {2017},
     volume = {60},
     number = {4},
     doi = {10.4153/CMB-2017-002-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-002-9/}
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