SOME REMARKS CONCERNING FINITELY SUBADDmVE OUTER MEASURES WITH APPUCATIONS

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 ofthe theory ofinner measures, their construction, and the relationship oftheir 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.