ABSTRACT
In this section, we investigate the relationship between convergence in law of a sequence of random vectors and convergence of expectations of functions of the vectors. The basic result is that https://www.w3.org/1998/Math/MathML"> X n → ℒ X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136288/c12c5089-77f8-4e14-84a1-364a5e26ae30/content/eq105.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> if and only if Eg(X n ) → Eg(X) for all continuous bounded functions g. We conclude with the Continuity Theorem that relates convergence in law of a sequence of random vectors with convergence of the corresponding characteristic functions.
