On the Rademacher Series
In this note we give simple proofs of some of the inequalities on Rademacher series given by M. Ledoux and M. Talagrand, , ch.4.1, S.J. Montgomery -Smith, , and by P. Hitczenko, . 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.
KeywordsBanach Space Independent Random Variable Convergent Series Good Constant Polynomial Chaos
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