A tiling property for actions of amenable groups along Tempelman Følner sequences

• Autorzy: Botersky, Jonathan , Zomback, Jenna
• Języki publikacji: EN

Abstrakty

EN

We show that a certain tiling property (which directly implies the pointwise ergodic theorem) holds for pmp actions of amenable groups along increasing Tempelman Følner sequences, thus providing a short and combinatorial proof of the corresponding pointwise ergodic theorem.

Słowa kluczowe

EN

pointwise ergodic theorem; tiling property; Tempelman Følner

• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2024
• Tom: Vol. 72, no 1
• Strony: 7--16
• Opis fizyczny: Bibliogr. 10 poz.,

Twórcy

autor

Botersky, Jonathan

• Department of Mathematics, Harvard University Cambridge, MA, USA,

autor

Zomback, Jenna

• Department of Mathematics, University of Maryland, College Park, MD, USA,

Bibliografia

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• [3] [Hoc07] M. Hochman, Averaging sequences and abelian rank in amenable groups, Israel J. Math. 158 (2007), 119–128.
• [4] [KP06] M. Keane and K. Petersen, Easy and nearly simultaneous proofs of the Ergodic Theorem and Maximal Ergodic Theorem, in: Dynamics and Stochastics,
• [5] IMS Lecture Notes Monogr. Ser. 48, Inst. Math. Statist., Beachwood, OH, 2006, 248–251.
• [6] [Lin01] E. Lindenstrauss, Pointwise theorems for amenable groups, Invent. Math. 146 (2001), 259–295.
• [7] [OW83] D. Ornstein and B. Weiss, The Shannon–McMillan–Breiman theorem for a class of amenable groups, Israel J. Math. 44 (1983), 53–60.
• [8] [Tem67] A. A. Tempel’man, Ergodic theorems for general dynamical systems, Soviet Math. Dokl. 8 (1967), 1213–1216.
• [9] [Tse18] A. Tserunyan, A descriptive set theorist’s proof of the pointwise ergodic theorem, arXiv:1805.07365 (2018).
• [10] [Wei03] B. Weiss, Actions of amenable groups, in: Topics in Dynamics and Ergodic Theory, London Math. Soc. Lecture Note Ser. 310, Cambridge Univ. Press, Cambridge, 2003, 226–262.

Identyfikatory

DOI

10.4064/ba230330-26-2