A classical result due to Eagleson states (in particular) that if appropriately normalized Birkhoff sums generated by a measurable function and an ergodic probability preserving transformation converge in distribution, then they also converge in distribution with respect to any probability measure which is absolutely continuous with respect to the invariant one. In this note, we prove several quantitative and infinite-dimensional versions of Eagleson's theorem for some classes of non-stationary stochastic processes which satisfy certain type of decay of correlations.

中文翻译：

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关于非平稳设置中的伊格森定理

由于 Eagleson 声明的经典结果（特别是），如果由可测量函数和遍历概率保持变换生成的适当归一化 Birkhoff 和在分布上收敛，那么它们在分布上也收敛于任何绝对连续的概率测度到不变的。在这篇笔记中，我们证明了伊格尔森定理的几个定量和无限维版本，用于满足某些类型的相关性衰减的非平稳随机过程。