Asmar, Nakhlé; Berkson, Earl; Gillespie, Thomas Alastair Transference of almost everywhere convergence. (Transfert de la convergence presque partout.) (French) Zbl 0796.43002 C. R. Acad. Sci., Paris, Sér. I 315, No. 13, 1389-1392 (1992). The authors show that if \(R\) is a representation of a locally compact abelian group \(G\) in \(L^ p(\Omega,\mu)\), then under certain conditions on \(R\) the sequence \(H_{k_ n}g=\int_ Gk_ n(u)R_{-u}g d\lambda(u)\) converges a.e. for every \(g \in L^ p(\Omega,\mu)\) whenever the sequence \(\{k_ n * f\}\) converges a.e. for every \(f \in L^ p(G)\), where \(\lambda\) is Haar measure of \(G\). Reviewer: V.V.Peller (Manhattan) Cited in 1 Review MSC: 43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) 28D99 Measure-theoretic ergodic theory Keywords:transference; ergodic theory; representation; locally compact abelian group; Haar measure PDFBibTeX XMLCite \textit{N. Asmar} et al., C. R. Acad. Sci., Paris, Sér. I 315, No. 13, 1389--1392 (1992; Zbl 0796.43002)