Large deviations for random vectors for certain classes of sets. II (Q1056979)

The analogues of \textit{V. A. Statulevičius'} lemma on large deviations [Z. Wahrscheinlichkeitstheor. Verw. Geb. 6, 133-144 (1966; Zbl 0158.362)] are proved for a random finite-dimensional vector \(\xi \in R^ s\). The classes of sets in \(R^ s\) for which the results of the paper are proved have been introduced by \textit{L. V. Osipov}, Mat. Zametki 31, 147- 155 (1982; Zbl 0488.60036). Applications to sums of independent random vectors are given.