Compactness in the theory of large deviations (Q1890710)

Large deviation principles are expressed as the vague or narrow convergence of sequences of the set functions called capacities. As an application, a short proof of Gärtner-Ellis criterion for the large deviation principle is given. The capacity methods introduced in the paper are also used in forthcoming papers [\textit{G. L. O'Brien}, Sequences of capacities, with connections to large-deviation theory, J. Theor. Probab. (to appear) and \textit{W. Bryc} and \textit{A. Dembo}, Large deviations and strong mixing, Ann. Inst. Henri Poincaré, Probab. Stat. (to appear)].