Vol. 23, No. 3, 1967

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ISSN: 0030-8730
On a theorem of Nikodym with applications to weak convergence and von Neumann algebras

Richard Brian Darst

Vol. 23 (1967), No. 3, 473–477
Abstract

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: supμT|μ(E)| < ,E S, then it is uniformly bounded: supμT(supES|μ(E)|) < .

Mathematical Subject Classification
Primary: 46.65
Secondary: 28.00
Milestones
Received: 22 March 1967
Published: 1 December 1967
Authors
Richard Brian Darst