The Khinchin-Kahane and Lévy inequalities for abelian metric groups, and transfer from normed (abelian semi)groups to Banach spaces (Q6136375)

One of the main results of the paper is a generalization of the Khinchin-Kahane inequality to arbitrary metric abelian groups (Theorem 2.7). In the process of proving Theorem 2.7, the authors provide an extension of Lévy's inequality (Theorem 2.10). Moreover, in the paper it is formulated and proved the ``transfer principle'', which allows one to take random variables and their probability/functional analysis from a subclass of abelian metric semigroups to Banach spaces (Theorem 3.3).