Ultralimits of Birkhoff averages

2018/05/24 by Carvalho, Maria, Moreira, Fernando
#03H05 #28A25 #37A30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1805.09715

Abstract

Given a compact metric space X and a probability measure in the σ-algebra of Borel subsets of X, we will establish a dominated convergence theorem for ultralimits of sequences of integrable maps and apply it to deduce a non-standard ergodic-like theorem for any probability measure.

Related

• Slow convergences of ergodic averages
• Convergence and divergence of averages along subsequences in certain Orlicz spaces
• Slow convergence of Birkhoff ergodic averages
• Quantitative Quasiperiodicity
• Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity