A Limit Theorem for Solutions of Inequalities

Let H ( p ) be the set { x ∈ X : h ( x ) ≤ p } where h is a real‐valued lower semicontinuous function on a locally compact separable metric space X . This paper presents a general limit theorem for the sequence of random sets H n ( p ) = { x ∈ X : h n ( x ) ≤ p } n ≥ 1, where h n , n ≥ 1, are functions that estimate h