Generalizations of the Nikodym boundedness and Vitali-Hahn-Saks theorems

[摘要] Generalizations of the Nikodym boundedness and Vitali-Hahn-Saks theorems for scalar-valued measures on rings of sets that are in general not sigma-rings are presented. As a consequence, the rings of subsets of N with density zero and uniform density zero are shown to have the Nikodym property. In addition, vector measure generalizations of the Vitali-Hahn-Saks theorem are given. (C) 2004 Elsevier Inc. All rights reserved.

[发布日期] 2004-12-15