On heredity of strongly proximal actions

C. Robinson Edward Raja

Address. Stat-Math Unit, Indian Statistical Institute, 8th Mile Mysore Road, R. V. College Post, Bangalore - 560 059, India

E-mail: creraja@isibang.ac.in, raja_robinson@hotmail.com

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.

AMSclassification. 37B05, 60B05.

Keywords. Proximal and strongly proximal actions, and probability measures.