Normal approximation of a functional of a Gaussian field

The asymptotic normality of a functional of a strongly correlated Gaussian random field having the meaning of the random volume of a bounded realization of the field over a parallelepiped or triangle is established in this paper. In addition some problems of geometric probabilities are solved: the distribution density of the distance between independent random vectors having uniform distribution in a rectangle or triangle is found.Translated from Teoriya Sluchainykh Protsessov, No. 16, pp. 55–60, 1988.