Failure of the L¹ pointwise ergodic theorem for\n \PSL₂(\ℝ)

2019/01/04 by Lewis Bowen, Bowen, Lewis, Peter Burton +1
Economics, Econometrics and Finance · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1901.01299

openalex publication_date 2019/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Amos Nevo established the pointwise ergodic theorem in L^p for\nmeasure-preserving actions of \PSL₂(\ℝ) on probability\nspaces with respect to ball averages and every p>1. This paper shows by\nexplicit example that Nevo's Theorem cannot be extended to p=1.\n

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