Sharp inequalities involving multiplicative chaos sums

The present note is an addition to the author’s recent paper[44], concerning general multiplicative systems of random variables. Using somelemmas and the methodology of [13], we obtain a general extremal inequality,with corollaries involving Rademacher chaos sums and those analogues for multiplicativesystems. In particular we prove that a system of functions generated bybounded products of a multiplicative system is a convergence system.