Convergence in Measure and in Category

W. Orlicz in 1951 has observed that if {f_n(·, y)}_n∈N converges in measure to f(·, y) for each y ∈ [0, 1], then {f_n}_n∈N converges in measure to f on [0, 1] × [0, 1]. The situation is different for the convergence in category even if we assume the convergence in category of sequences {f_n(·, y)}_n∈N for each y ∈ [0, 1] and {f_n(x, ·)}_n∈N for each x ∈ [0, 1].