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.

翻译：本文概括了Lindeberg-Feller和Lyapunov对Hilbert空间的中央限制理论。 顺便一提,它证明Lindeberg- Feller和Lyapunov的条件迫使随机变量的收集形成一个精密的、紧凑的地形结构。 这些结果将帮助研究人员进行非参数推论,给他们一套简单的条件,既检查无症状的正常性,也检查无限维度环境中的紧凑性和界限性。