Some theorems on first-order asymptotic behavior of probabilities of large deviations of empirical probability measures are proved. These theorems extend previous results due to Borovkov, Hoadley and Stone. A multivariate analogue of Chernoff's theorem and a large deviation result for trimmed means are obtained as particular applications of the general theory.
"Large Deviation Theorems for Empirical Probability Measures." Ann. Probab. 7 (4) 553 - 586, August, 1979. https://doi.org/10.1214/aop/1176994984