Whenever we have a measure function α defined on some set M of subsets of a set T, we may determine a binary relation Q between the elements of M by defining, for all members A and B of M, AQB if and only if α(A) ≤ α(B). Using such a binary relation, we may derive certain measure theoretic properties independently of the real number system. In particular, if we use what might be termed a process of completion, we may construct, from a system of Borel sets, not only a system of Lebesgue measurable sets, but, in general, a somewhat larger system.
Proceedings of the Iowa Academy of Science
©1962 Iowa Academy of Science, Inc.
Sanderson, Donovan F.
"On the Construction of the Measurable Sets,"
Proceedings of the Iowa Academy of Science, 69(1), 444-445.
Available at: https://scholarworks.uni.edu/pias/vol69/iss1/69