A LIMIT-THEOREM FOR SOLUTIONS OF INEQUALITIES

Let H(p) be the set {x is an element of X:h(x) less than or equal to 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 is an element of X :h(n)(x) less than or equal to p}, n greater than or equal to 1, where h(n), n greater than or equal to 1, ape functions that estimate h.