Continuous linear maps positive on increasing continuous functions

A. Katsaras
1977 Pacific Journal of Mathematics  
Let E be a locally convex lattice and X a completely regular space ordered by a closed order relation. We study E-valued (resp. E'-valued) measures on an algebra or a σ-algebra of subsets of X with respect to which every increasing continuous real (resp. £-valued) function with relatively compact range has positive integral. Each V k is increasing and the sets A o , A b , A n -{ form a partition of X into members of B(X). Since |/-fc/n | ^ l//t on A fc , we have ί J fdm--Σkm(A k )
doi:10.2140/pjm.1977.70.189 fatcat:jjcbxw3sijdl3pzm3gmiw7o3z4