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The main aim of this paper is to prove that the logarithmic means of the double Walsh–Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of log ( 2 ), the set of functions for which quadratic logarithmic means of the double Walsh–Fourier series converge in measure is of first Baire category.

Convergence in Measure of Logarithmic Means of Double Walsh–Fourier Series