Vol. 48, No. 2, 1973

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Separative relations for measures

A. P. Morse and Donald Chesley Pfaff

Vol. 48 (1973), No. 2, 451–471

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.

Mathematical Subject Classification 2000
Primary: 28A10
Received: 15 October 1970
Published: 1 October 1973
A. P. Morse
Donald Chesley Pfaff