The metric of large deviation convergence (Q1592276)

A metric space of set functions, such that a sequence \(\{P_n\}\) of Borel probability measures on this metric space satisfies the full large deviation principle (LDP) with speed \(\{a_n\}\) and good rate function \(I\) if and only if the sequence \(\{p_n^{a_n}\}\) converges to set function \(e^{-I}\), is constructed. Properties related to the LDP and weak convergence are characterized in terms of a metric space.