Uniform continuity of a family of weakly regular set functions in a topological space. (Q1889505)

The paper is devoted to a generalization of a Grothendieck's theorem in the case where the set functions are weakly regular and nonadditive. Set functions are considered with values in a topological space, but a sufficient illustration of this study is not given. There are very few and almost trivial examples of the considered generalization and its advantage and usefulness are not outlined. Detailed definitions and proofs of theorems are given in the article.