Geodesic
Necessity of Cramer's, Linnik's and Statulevi\u cius conditions for large deviation probabilities
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 9-16

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In this paper the necessity of Cramer's, Linnik's and Statulevic̆ius conditions is considered in theorems for large deviations probabilities. It is shown also that Statulevic̆ius condition is a generalization of Cramer's and Linnik's conditions. 
@article{ZNSL_1999_260_a0,
     author = {N. N. Amosova},
     title = {Necessity of {Cramer's,} {Linnik's} and {Statulevi\u} cius conditions for large deviation probabilities},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {9--16},
     publisher = {mathdoc},
     volume = {260},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a0/}
}
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N. N. Amosova. Necessity of Cramer's, Linnik's and Statulevi\u cius conditions for large deviation probabilities. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 9-16. http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a0/