On convergence and divergence of Fourier series and Féjer means with applications to Lebesgue and Vilenkin-Lebesgue points (Q6611682)

This is an expository article that discusses recent results about divergence on a set of measure zero of Fourier series with respect to Vilenkin systems and also about the Vilenkin-Lebesgue points of functions. In particular, it is mentioned that the following two results immediately follow from already known, recently obtained, results:\N\NTheorem. If \(E \subset G_m\) is a set of measure zero, then there exists a function \(f\in L_1 (G_m)\) such that none of the points of \(E\) is a Lebesgue point of \(f\).\N\NTheorem. If \(E \subset G_m\) is a set of measure zero, then there exists a function \(f\in L_1 (G_m)\) such that none of the points of \(E\) is a Vilenkin- Lebesgue point of \(f\).\N\NFor the entire collection see [Zbl 1544.35009].