Spatial recurrence for ergodic fractal measures


Journal Article

© Instytut Matematyczny PAN, 2019 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 adapt-edness 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.

Full Text

Duke Authors

Cited Authors

  • Dym, N

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 248 / 1

Start / End Page

  • 1 - 29

Electronic International Standard Serial Number (EISSN)

  • 1730-6337

International Standard Serial Number (ISSN)

  • 0039-3223

Digital Object Identifier (DOI)

  • 10.4064/sm8715-3-2018

Citation Source

  • Scopus