International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 653-669

Some remarks concerning finitely Subadditive outer measures with applications

John E. Knight

Department of Mathematics, Long Island University, Brooklyn Campus, University Plaza, Brooklyn 11201, New York, USA

Received 21 November 1996; Revised 29 October 1997

Copyright © 1998 John E. Knight. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion of the theory of inner measures, their construction, and the relationship of their properties to those of an associated finitely subadditive outer measure. In particular, the interconnections between the measurable sets determined by both the outer measure and its associated inner measure are examined. Finally, several applications of the general theory are given, with special attention being paid to various lattice related set functions.