Existence of measures invariant with respect to a semigroup of continuous open mappings of a locally compact topological space
Let \(S\) be a semigroup of continuous and open mappings of a locally compact space \(X\). The purpose of the paper is to establish conditions under which there exists a left \(S\)-invariant measure on \(X\). The first theorem only establishes the existence of such a measure whose support is an orbit in \(X\). Here an orbit is defined to be a set closed under the smallest equivalence relation containing all pairs \((x,s (x))\). There are then three corollaries which establish conditions under which there is such a measure with support the whole of \(X\).
scientific article; zbMATH DE number 846501