Operators, martingales, and measures on projective limit spaces
arXiv:math/0407517
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.
Dedicated to the memory of Shizuo Kakutani. In v3, some introductory material and additional references are added. 20 pages in "amsart" LaTeX document class; uses "diagrams" package