In 1987 Harris proved-among others that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ L_p such that its triangular Walsh-Fourier series does not converge almost everywhere. In this paper we prove that the set of the functions from the space L_p(II²) (1 ≤ p < 2) with subsequence of triangular partial means \(S_{2^A}^\Delta(f)\) of the double Walsh-Fourier series convergent in measure on II² is of first Baire category in L_p(II²). We also prove that for each function f ∈ L₂(II²) a.e. convergence \(S_{a(n)}^\Delta (f) \rightarrow f\) holds, where a(n) is a lacunary sequence of positive integers.

在1987年哈里斯证明-等等，对于每个1个≤ p <2存在二维函数˚F ∈大号_p，使得其三角形沃尔什-傅立叶级数不收敛几乎无处不在。在本文中，我们证明了该组的从所述空间的功能大号_p（II ²）（1个≤ p与三角形部分手段序列<2）\（S_ {2 ^ A} ^ \德尔塔（F）\）的在II ²上收敛的双重Walsh-Fourier级数是L _p（II ²）中的第一类Baire类。我们也证明了对每个功能˚F ∈大号₂（II ²）AE收敛\（S_ {A（N）} ^ \德尔塔（F）\ RIGHTARROW˚F\）成立，其中一个（Ñ）为正整数的缺位序列。