This article is cited in 1 paper

A probability inequality

A. V. Prokhorov

M. V. Lomonosov Moscow State University

Abstract: The inequalities due to S. N. Bernshtein for the probability of $P(|Y_n|\ge r)$, where $|Y_n|$ is the length of the vector of the normalized sum of the independent and identically distributed vectors and $r>0$ is an arbitrary quantity are extended to the case of two and three dimensions. Some results are also given in the multidimensional case.

UDC: 519.2

Received: 15.03.1968

 English version: Mathematical Notes, 1968, 3:6, 467–472

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