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On a theorem of Nikodym
with applications to weak convergence and von Neumann
algebras
Richard Brian Darst |
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Vol. 23 (1967), No. 3, 473–477
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Abstract |
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The theorem of the title is a “striking improvement of the principle of uniform boundedness” in the space of countably additive measures on a sigma algebra. It says that if a set T of countably additive measures μ on a sigma algebra S is pointwise bounded: supμ∈T|μ(E)| < ∞,E ∈ S, then it is uniformly bounded: supμ∈T(supE∈S|μ(E)|) < ∞. |
Mathematical Subject Classification
Primary: 46.65
Secondary: 28.00
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Milestones
Received: 22 March 1967
Published: 1 December 1967
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Authors |
| Richard Brian Darst | |
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