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arXiv · 1509.05938

On pointwise ergodic theorems for infinite measure

Vladimir Chilin·Dogan Comez·Semyon Litvinov
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Abstract

For a Dunford-Schwartz operator in the $L^p-$space, $1\leq p< \infty$ , 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.

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Vladimir Chilin, Dogan Comez, Semyon Litvinov. 2015-09-19. On pointwise ergodic theorems for infinite measure. https://arxiv.org/abs/1509.05938

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