### Non-Homogeneous Markov Chains: Tail Idempotents, Tail Sigma-Fields and Basis.

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Choquet and Deny considered on an abelian locally compact topological group the representation of a measure $P$ as the convolution product of itself and a finite measure $Q:P={P}^{*}Q$. In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions $P$ of the above equation which are relatively invariant on the support of $Q$. A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results on the above...

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