Geodesic
On heredity of strongly proximal actions
Archivum mathematicum, Tome 39 (2003) no. 1, pp. 51-55
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We prove that action of a semigroup $T$ on compact metric space $X$ by continuous selfmaps is strongly proximal if and only if $T$ action on ${\mathcal P}(X)$ is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.
We prove that action of a semigroup $T$ on compact metric space $X$ by continuous selfmaps is strongly proximal if and only if $T$ action on ${\mathcal P}(X)$ is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.
Classification : 37A15, 37B05, 54H20, 60B05
Keywords: proximal and strongly proximal actions; probability measures 
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     author = {Raja, C. Robinson Edward},
     title = {On heredity of strongly proximal actions},
     journal = {Archivum mathematicum},
     pages = {51--55},
     year = {2003},
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     zbl = {1110.37005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2003_39_1_a4/}
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Raja, C. Robinson Edward. On heredity of strongly proximal actions. Archivum mathematicum, Tome 39 (2003) no. 1, pp. 51-55. http://geodesic.mathdoc.fr/item/ARM_2003_39_1_a4/

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[P] Parthasarathy K. R.: Probability Measures on Metric Spaces. Academic Press, New York-London, 1967. | MR | Zbl