On a general Kac-Rice formula for the measure of a level set

Diego Armentano, Jean-Marc Azaïs, José Rafael León

Let $X(\cdot )$ be a random field ${\mathbb{R}}^D\to {\mathbb{R}}^d$, $D\ge d$. We first studied the level set $X^{-1}(u)$, $u\in {\mathbb{R}}^d$. In particular we gave a weak condi…