International Journal of Mathematics and Mathematical Sciences 
Volume 19 (1996), Issue 3, Pages 461-472
doi:10.1155/S016117129600066X

Finitely subadditive outer measures, finitely superadditive inner measures and their measurable sets

P. D. Stratigos

 Department of Mathematics, Long Island University, Brooklyn 11201, NY, USA
Received 24 February 1994; Revised 28 April 1995

Abstract

Consider any set X. A finitely subadditive outer measure on P(X) is defined to be a function v from P(X) to R such that v(ϕ)=0 and v is increasing and finitely subadditive. A finitely superadditive inner measure on P(X) is defined to be a function p from P(X) to R such that p(ϕ)=0 and p is increasing and finitely superadditive (for disjoint unions) (It is to be noted that every finitely superadditive inner measure on P(X) is countably superadditive).

This paper contributes to the study of finitely subadditive outer measures on P(X) and finitely superadditive inner measures on P(X) and their measurable sets.