Ergodic theorem for random measures, homogeneous in a broad sense (Q1063942)

Suppose \(\mu\) is a second order stationary random measure on \({\mathbb{R}}^ d\), and let m denote d-dimensional Lebesgue measure. The ergodic theorem proved asserts that \(m(B_ n)^{-1}\mu (B_ n)\) converges in mean square for a class of directed nets of Borel subsets \(B_ n\) of \({\mathbb{R}}^ d\), called in this paper \(\alpha\)-ergodic nets.