Lebesgue points and Cesaro summability of higher dimensional Fourier series over a cone

We introduce a new concept of Lebesgue points, the so-called.Lebesgue points, where omega > 0. As a generalization of the classical Lebesgue's theorem, we prove that the Cesaro means sigma(a)(n)f of the Fourier series of a multidimensional function f is an element of L-1(T-d) converge to f at each omega-Lebesgue point (0 < omega < alpha) as n -> 8.