Consider a semigroup action on a set. We derive conditions, in terms of the induced action of the semigroup on {0,1}-valued probability charges, which ensure that all invariant probability charges are strongly continuous.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-1-9, author = {Harald Luschgy and S\l awomir Solecki}, title = {Strong continuity of invariant probability charges}, journal = {Colloquium Mathematicae}, volume = {100}, year = {2004}, pages = {135-142}, zbl = {1073.28002}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-1-9} }
Harald Luschgy; Sławomir Solecki. Strong continuity of invariant probability charges. Colloquium Mathematicae, Tome 100 (2004) pp. 135-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm101-1-9/