On Convergence and Divergence of Fourier Series and Féjer Means with Applications to Lebesgue and Vilenkin-Lebesgue Points

In the first part of this paper review results concerning almost everywhere convergence and divergence on the set of measure zero of partial sums and Féjer means with respect to Vilenkin and trigonometric systems. By using this information we prove that for any set E of measure zero there exists a function \(f\in L_1(G_m)\) such that each \(x\in E\) is not Lebesgue and Vilenkin-Lebesgue points.