Abstract:Varadhan's integration theorem, one of the corner stones of large-deviation theory, is generalized to the context of capacities. The theorem appears valid for any integral that obeys four linearity properties. We introduce a collection of integrals that have these properties. Of one of them, known as the Choquet integral, some continuity properties are established as well.
Keywords: capacities, large deviations, Choquet integral, Varadhan's integration theorem
AMS Subject Classification: 28A12, 28A25, 60F10