On local ergodic convergence of semi-groups and additive processes

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3 Scopus citations

Abstract

We prove the local ergodic theorem in L: Let {T t}t>0 be a strongly continuous semi-group of positive operators on L 1. If T t is continuous at 0, then e{open}-1 0 F T 1 * f(x)dt→T 0 * f(x) a.e., for every f∈L. The technique shows how to obtain the L p local ergodic theorems from the L 1-contraction case. It applies also to differentiation of L p additive processes. The n-dimensional case, which is new, is proved by reduction to the n-dimensional L 1-contraction case, solved by M. Akcoglu and A. del Junco.

Original languageEnglish
Pages (from-to)300-308
Number of pages9
JournalIsrael Journal of Mathematics
Volume42
Issue number4
DOIs
StatePublished - 1 Dec 1982

ASJC Scopus subject areas

  • Mathematics (all)

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