Convergence in Measure of Strong logarithmic means of double Fourier series

N"orlund strong logarithmic means of double Fourier series acting from space $$ into space $L_p(\mathbb{T}$ are studied. The maximal Orlicz space such that the N"o% rlund strong logarithmic means of double Fourier series for the functions from this space converge in two-dimensional measure is found.