Almost Everywhere Convergence of Riesz-Raikov Series

Let T be a d×d matrix with integer entries and with eigenvalues >1 in modulus. Let f be a lipschitzian function of positive order. We prove that the series ${\displaystyle {\sum }_{n=1}^{\infty }{c}_{n}f\left(T^{n}x\right)}$ converges almost everywhere with respect to Lebesgue measure provided that ${\displaystyle {\sum }_{n=1}^{\infty }{\left|c_n\right|}^2{\log }^{2}n<\infty }$.