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Document Type

Research

Abstract

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.

Publication Date

1962

Journal Title

Proceedings of the Iowa Academy of Science

Volume

69

Issue

1

First Page

444

Last Page

445

Copyright

© Copyright 1962 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

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