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Transference of almost everywhere convergence. (Transfert de la convergence presque partout.) (French) Zbl 0796.43002

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 \(G\).

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
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