Finitely additive set functions into a topological group

The properties of finitely additive set functions defined on a ring S with values in an Abelian topological group are studied. In particular, a condition under which the property of uniform absence of the escaping load (UAEL) is preserved under the extension of a set function from a ring R to an extending ring S R is established.Translated from Matematicheskie Zametki, Vol. 21, No. 6, pp. 847–854, June, 1977.