On random surface area

Consider a random smooth Gaussian field $G(x)\colon F\to\mathbb R$, where $F$ is a compact in $\mathbb R^d$. We derive a formula for average area of a surface set by the equation $G(x)=0$ and give some applications. As an auxiliary result we obtain an integral expression for area of a surface induced by zeros of any non-random smooth field. Bibl. 13 titles.