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Nörlund strong logarithmic means of double Fourier series acting from space L log L \(\left( {\mathbb{T}^2 } \right)\) into space L  p  \(\left( {\mathbb{T}^2 } \right)\), 0 < p < 1, are studied. The maximal Orlicz space such that the Nörlund strong logarithmic means of double Fourier series for the functions from this space converge in two-dimensional measure is found.

Convergence in measure of strong logarithmic means of double Fourier series