Spatial recurrence for ergodic fractal measures
Tom 248 / 2019
Studia Mathematica 248 (2019), 1-29
MSC: Primary 28A80.
DOI: 10.4064/sm8715-3-2018
Opublikowany online: 11 February 2019
Streszczenie
We study the invertible version of Furstenberg’s ‘ergodic CP shift systems’, which describe a random walk on measures on Euclidean space. These measures are by definition invariant under a scaling procedure, and satisfy a condition called adaptedness under a ‘local’ translation operation. We show that the distribution is in fact non-singular with respect to a suitably defined translation operator on measures, and derive discrete and continuous pointwise ergodic theorems for the translation action.
