Pointwise ergodic theorems in symmetric spaces of measurable functions

2016/12/17 by Chilin, Vladimir, Comez, Dogan, Litvinov, Semyon
#37A30(secondary) #47A35(primary) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1612.05802

Abstract

For a Dunford-Schwartz operator in a fully symmetric space of measurable functions of an arbitrary measure space, we prove pointwise convergence of the conventional and weighted ergodic averages.

Related

• On pointwise ergodic theorems for infinite measure
• Almost uniform and strong convergences in ergodic theorems for symmetric\n spaces
• Local ergodic theorems in symmetric spaces of measurable operators
• Almost Uniform Convergence in Noncommutative Dunford-Schwartz Ergodic Theorem for p>1
• Individual ergodic theorems for infinite measure