  The present note is an essential addition to the author's arxiv paper
arXiv:2001.01070, concerning general multiplicative systems of random
variables. Using some lemmas and the methodology of \cite{Kar4}, we obtain a
general extreme inequality, with corollaries involving Rademacher chaos sums
and those analogues for multiplicative systems. In particular we prove that a
system of functions generated by bounded products of a multiplicative system is
a convergence system.
