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Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment

Christopher M. Wedrychowicz — 2011

Annales de l’institut Fourier

Bellow and Calderón proved that the sequence of convolution powers μ n f ( x ) = k μ n ( k ) f ( T k x ) converges a.e, when μ is a strictly aperiodic probability measure on such that the expectation is zero, E ( μ ) = 0 , and the second moment is finite, m 2 ( μ ) < . In this paper we extend this result to cases where m 2 ( μ ) = .

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