Integral representations and refinement-unboundedness
William D. L. Appling · Proceedings of the American Mathematical Society · 1968
Suppose U is a set, F is a field of subsets of U, p is the set of all real-valued functions defined on F, $A is the set of all bounded and finitely additive elements of p, p+ is the set of all nonnegative-valued elements of p, and pi -pAr^p+.Suppose p. is in pA.Definition.If 3H is a number set and £ is in pA, then the statement that £ is p.-dense in 3TC means that if V is in F and 0<c, then there is a subdivision @ of V and a function n from (5 into 3ft such that