Extensions of (weakly) null-additive, monotone set functions from rings to generated algebras

摘要

This paper shows that the greatest and least monotone extensions of a null-additive [resp weakly null-additive], monotone set function from a ring of subsets to the algebra generated by the ring are null-additive [resp. weakly null-additive]. In addition, the paper characterizes all the (weakly) null-additive, monotone extensions.