Lebesgue and Vilenkin-Lebesgue points and a.e. Convergence of T means with respect to Vilenkin systems of integrable functions

Abstract

In this paper we derive converge of $T$ means of Vilenkin-Fourier series with monotone coefficients of integrable functions in Lebesgue and Vilinkin-Lebesgue points. Moreover, we discuss pointwise and norm convergence in $L_p$ norms of such $T$ means.