Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems |
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| Authors: | Christopher E Stuart Paul Abraham |
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| Institution: | aDepartment of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA;bDepartment of Mathematical Sciences, Kent State Stark Campus, Canton, OH 44720, USA |
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| Abstract: | Generalizations of the Nikodym boundedness and Vitali–Hahn–Saks theorems for scalar-valued measures on rings of sets that are in general not σ-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. |
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