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A simple example in Section 2.2 illustrated that the notions of nullcontinuity and σ-continuity are not identical (Example 2.2.6). We want to investigate the connection more thoroughly. Clarifying the connection between nullcontinuity and σ-continuity will also help illuminate, in the next section, the structure of the space of real measures on a ring of sets. We lay out a few preliminary results first.
KeywordsPositive Measure Vector Lattice Real Measure Finite Variation Disjoint Family
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