**György Gát, Ushangi Goginava, George Tkebuchava**

##
Convergence in Measure of Logarithmic Means of Double Walsh-Fourier Series

**Abstract:**

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 $L\log L(I^{2})$,
the set of functions for which quadratic logarithmic means of the double
Walsh-Fourier series converge in measure is of first Baire category.

**Keywords:**

Double Walsh-Fourier series, Orlicz space, convergence in measure.

**MSC 2000:** 42C10