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Operators, martingales, and measures on projective limit spaces

Dorin Ervin Dutkay·Palle E. T. Jorgensen
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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_\infinity(r). We show that the invariant measures on X_\infinity(r) correspond in a one-to-one fashion to measures on X which satisfy two identities. Moreover, we identify those special measures on X_\infinity(r) which are associated via our correspondence with a function V on X, a Ruelle transfer operator R_V, and an equilibrium measure μ_V on X.

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Dorin Ervin Dutkay, Palle E. T. Jorgensen. 2004-12-07. Operators, martingales, and measures on projective limit spaces. https://arxiv.org/abs/math/0407517

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