Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Kaczmarz-Fourier series (Q657327)

Summary: The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of \(L \log^+ L(I^2)\), the set of the functions the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series of which converge in measure is of first Baire category.