On pointwise ergodic theorems for infinite measure
Functional Analysis
2016-09-21 v2
Abstract
For a Dunford-Schwartz operator in the space, , of an arbitrary measure space, we prove pointwise convergence of the conventional and Besicovitch weighted ergodic averages. Pointwise convergence of various types of ergodic averages in fully symmetric spaces of measurable functions with non-trivial Boyd indices is studied. In particular, it is shown that for such spaces Bourgain's Return Times theorem is valid.
Cite
@article{arxiv.1509.05938,
title = {On pointwise ergodic theorems for infinite measure},
author = {Vladimir Chilin and Dogan Comez and Semyon Litvinov},
journal= {arXiv preprint arXiv:1509.05938},
year = {2016}
}
Comments
This paper has been withdrawn by the author due to a crucial error in the last section