International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 653-669
doi:10.1155/S016117129800091X

Some remarks concerning finitely subadditive outer measures with applications

Abstract

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.