The essential divergence in measure of function sequences and series (Q1878560)

The authors study divergence with respect to measure of functional sequences on the \(\sigma\)-finite measure space \((X,\Sigma,\nu)\). Besides, it is proved that under certain conditions for the Fourier series, whose cubic partial sums diverge unboundedly with respect to measure, there exists a Fourier series in the same system, whose cubic partial sums diverge essentially with respect to measure on a set of complete measure.