This article is cited in 6 papers

The S. N. Bernstein inequalities in the multidimensional case

A. V. Prokhorov

M. V. Lomonosov Moscow State University

Abstract: Inequalities (2.2) and (2.3) are derived which are extensions of S. N. Bernstein's inequalities to the multidimensional case. Analysis of the inequalities obtained shows that their exponential factors are very close to those for the normal case (cf. (1.1) and (1.3)).

Received: 05.05.1968

 English version: Theory of Probability and its Applications, 1968, 13:3, 438–447

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