Distribution results for the occupation measures of continuous Gaussian fields

For a d-dimensional random field X(t) define the occupation measure corresponding to the level [alpha] by the Lebesgue measure of that portion of the unit cube over which X(t)[greater-or-equal, slanted][alpha]. Denoting this by M[X, [alpha]], it is shown that for sample continuous Gaussian fields as [alpha]-->[infinity], for a particular functional k[beta]. This result is applied to a variety of fields related to the planar Brownian motion, and for each such field we obtain bounds for k[beta].