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In this paper, we study the necessity of the Cramer, Linnik, and Statulevicius conditions in theorems on large-deviation probabilities. We also show that the Statulevicius condition is a generalization of the Cramer and Linnik conditions. Bibliography: 7 titles.

Necessity of the Cramer, Linnik, and Statulevičius Conditions for Large-Deviation Probabilities