When dealing with
Carathéodory (outer) measures, a natural problem arises: how does one determine a
nontrivial, interesting family of measurable sets? In particular cases of a metric or
topological nature, it has been customary to assume that the measure is additive on
sets which are a bit more than merely disjoint. The general approach of this paper,
purely set-theoretical in nature, emphasizes a relation R which “separates” sets, and
describes certain sets, constructed with the aid of R, which turn out to be
measurable whenever the measure is additive on sets which are separatively
related.
