On the Convergence of Product Moments

Abstract

Let Ⓗ be an abstract space and for every positive integer n let Fn, θ(x, y), θ ∈ Ⓗ, be a family of distribution n, 0 function s of random variables (Xn, Yn)θ, θ ∈ Ⓗ. For every θ ∈ Ⓗ, Eθg (Xn, Yn) will denote the expected value of the function g of (Xn, Yn )θ. The following proposition is proved.