Operators, martingales, and measures on projective limit spaces

Details Operators, martingales, and measures on projective limit spaces Operators, martingales, and measures on projective limit spaces

2004-07-29

arxiv.org/abs/math/0407517v3

Conform. Geom. Dyn. 9 (2005), 24-45

Mathematics

Classical Analysis and ODEs

Dedicated to the memory of Shizuo Kakutani. In v3, some introductory material and additional references are added. 20 pages in

Scientific paper

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 \mu_V on X.

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