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Given an increasing sequence of domains $(D_n) \\subset \\N^d$, a question is the convergence in distribution of the normalized sequence $|D_n|^{-\\frac12} \\sum_{{\\k} \\, \\in D_n} \\, f \\circ T^{\\,{\\k}}$, for $f \\in L^2_0(\\mu)$, where $T^{\\k}= T_1^{k_1} ... T_d^{k_d}$, ${\\k}= (k_1, ..., k_d) \\in {\\N}^d$. 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