Operators, martingales, and measures on projective limit spaces
Dorin Ervin Dutkay, Palle E. T. Jorgensen
Abstract
Let X be a compact Hausdorff space. We study finite-to-one mappings r:X->X, onto X, and measures on the corresponding projective limit space X∈finity(r). We show that the invariant measures on X∈finity(r) correspond in a one-to-one fashion to measures on X which satisfy two identities. Moreover, we identify those special measures on X∈finity(r) which are associated via our correspondence with a function V on X, a Ruelle transfer operator RV, and an equilibrium measure μV on X.
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