Akcoglu, M. A.; Falkowitz, M. A general local ergodic theorem in \(L_ 1\). (English) Zbl 0579.47004 Pac. J. Math. 119, 257-264 (1985). Let \(\{T_ t\}_{t>0}\) be a strongly continuous semi group of linear contractions on the \(L_ 1\) space of a measure space (X,\({\mathcal F},\mu)\). It is shown that if \(f\in L_ 1\) then \(\lim_{t\to 0^+}(1/t)\int^{t}_{0}T_ sf ds\) exists a.e. on X. Cited in 1 Document MSC: 47A35 Ergodic theory of linear operators 47D07 Markov semigroups and applications to diffusion processes 28D05 Measure-preserving transformations Keywords:strongly continuous semi group of linear contractions PDFBibTeX XMLCite \textit{M. A. Akcoglu} and \textit{M. Falkowitz}, Pac. J. Math. 119, 257--264 (1985; Zbl 0579.47004) Full Text: DOI