The Generalized Chernoff-Stein Lemma, Applications and Examples

In this manuscript we define the notion of "$\delta$-typicality" for both entropy and relative entropy, as well as a notion of $\epsilon$-goodness and provide an extension to Stein's lemma for continuous quantities as well as correlated setups. We apply the derived results on the Gaussian hypothesis testing problem where the observations are possibly correlated.