Non-singular $\mathbb {Z}^d$ -actions: an ergodic theorem over rectangles with application to the critical dimensions

We adapt techniques developed by Hochman to prove a non-singular ergodic theorem for $\mathbb {Z}^d$ -actions where the sums are over rectangles with side lengths increasing at arbitrary rates, and in particular are not necessarily balls of a norm. This result is applied to show that the critical di...

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Veröffentlicht in:	Ergodic theory and dynamical systems 2021-12, Vol.41 (12), p.3722-3739
Hauptverfasser:	DOOLEY, ANTHONY H., JARRETT, KIERAN
Format:	Artikel
Sprache:	eng
Schlagworte:	Ergodic processes Invariants Isomorphism Original Article Rectangles Theorems
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