The Lindeberg-Feller and Lyapunov Conditions in Infinite Dimensions: Asymptotic Normality and Compactness

This paper generalizes the Lindeberg-Feller and Lyapunov Central Limit Theorems to Hilbert Spaces. Along the way, it proves that the Lindeberg-Feller and Lyapunov conditions force collections of random variables into a nice bounded and compact topological structure. These results will help researchers do non-parametric inference by giving them a simple set of conditions for checking both asymptotic normality as well as compactness and boundedness in infinite-dimensional settings.