Spatial Recurrence for Ergodic Fractal Measures
نویسنده
چکیده
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 to 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.
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تاریخ انتشار 2014