Moment inequalities and the central limit theorem for integrals of random fields with mixing

Let X_u, uR^q, be a weakly dependent random field, EX_u=0, let be the Lebesque measure in R^q, let V_u be an increasing system of subsets in R^q, and let. One obtains a central limit theorem for _u and estimates for the moments E¦_n¦^t, t2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 39–47, 1985.