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We present several formulations of the large deviation principle for empirical measures in the V topology, depending on the initial distribution. The case V = B(S) is further studied.
We relate the rate functions introduced in Chapters 2 and 3 to the functions I and Isubindex ψ. We establish conditions for the equality I= Isubindex ψ. We introduce the conditions V.1′–V.4.
We obtain lower bounds for bounded vector-valued additive functionals and use them to obtain lower bounds for empirical measures. We prove a lower semicontinuity property of Λ.
We study large deviations for general vector-valued additive functionals. The relationship between large deviations for empirical measures and large deviations for additive functionals is discussed.