On vector-valued Dobrakov submeasures

TL;DR

This paper extends Dobrakov's theory of non-additive set functions to vector-valued submeasures on rings of sets, including their extensions in the sense of Drewnowski, advancing the mathematical framework of non-additive measures.

Contribution

It introduces the concept of vector-valued Dobrakov submeasures and explores their extensions, broadening the scope of non-additive measure theory.

Findings

Development of vector-valued Dobrakov submeasures

Extension of these submeasures in Drewnowski's sense

Advancement in non-additive measure theory

Abstract

Ivan Dobrakov has initiated a theory of non-additive set functions defined on a ring of sets intended to be a non-additive generalization of the theory of finite non-negative countably additive measures. These set functions are now known as the Dobrakov submeasures. In this paper we extend Dobrakov's considerations to vector-valued submeasures defined on a ring of sets. The extension of such submeasures in the sense of Drewnowski is also given.