On the Rademacher Series

Abstract

In this note we give simple proofs of some of the inequalities on Rademacher series given by M. Ledoux and M. Talagrand, [6], ch.4.1, S.J. Montgomery -Smith, [8], and by P. Hitczenko, [3]. We obtain better constants with proofs which can be useful in some other cases. As a corollary we prove a theorem of Kolmogorov on the lower estimates of the tail of sums of symmetric, independent random variables.