Abstract
Let K be a compact subset of R d and let m define a semi-dynamical system on M 1( K),, the space of probability measures on K, induced by a homogeneous Markov process. Let J( φ) be the prolongational limit set for φ ϵ M 1( K). The main result of the paper is the decomposition: support of J( φ) = ∪ {support of J( δ x ): x ϵ support φ}, where δ x is the Dirac measure at the point x.
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