Walsh-Lebesgue points of multi-dimensional functions

Walsh-Lebesgue points are introduced for higher dimensions and it is proved that a. e. point is a Walsh-Lebesgue point of a function f from the Hardy space H-1(i)[0,1)(d), where H-1(i)[0, 1)(d) superset of L(log L)(d-1)[0,1)(d) for all i = 1,..., d. Every function f epsilon H-1(i)[0, 1)(d) is Fejer summable at each Walsh-Lebesgue point. Similar theorem is verified for theta-summability.