  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.
