A Radon-Nikodym theorem in dimension lattices

Abstract

It is the primary purpose of this paper to prove that: if either a gage m or a dimension function D is given, then the remaining two mappings can be constructed so that the diagram is commutative; i.e., the equation m = poD holds. Moreover, if two of m, p, D are given, then the third satisfying m = poD is uniquely determined. (Author)