Lebesgue points of %$\ell _1%$-Cesàro summability of d-dimensional Fourier series

Abstract We generalize the classical Lebesgue’s theorem and prove that the %$\ell _1%$-Cesàro means of the Fourier series of the multi-dimensional function %$f\in L_1({{\mathbb {T}}}^d)%$ converge to f at each strong %$\omega %$-Lebesgue point.