We consider data that are dependent, but where most small sets of observations are independent. By extending Bernstein's inequality we prove a strong law of law numbers and an empirical process central limit theorem under bracketing entropy conditions.
Statistical Methodology | Statistical Theory
Lumley, Thomas, "An Empirical Process Limit Theorem for Sparsely Correlated Data" (June 2005). UW Biostatistics Working Paper Series. Working Paper 255.