An extension of a lemma of Wald

Abstract

We define a natural extension of the concept of expectation of a random variable y as follows: M ( y ) = a if there exists a constant − ∞ ≦ a ≦ ∞ such that if y 1 , y 2 , … is a sequence of independent identically distributed (i.i.d.) random variables with the common distribution of y then