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A
theorem on lattice ordered groups, results of Ptak, Namioka
and Banach, and a front-ended proof of Lebesgue’s theorem
Stephen Simons |
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Vol. 20 (1967), No. 1, 149–153
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Abstract |
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The main theorem in this paper is on (not necessarily commutative) lattice ordered groups, and is a generalization of a result on finitely additive set functions due to Namioka. Our result can be used to prove Ptak’s combinatorial theorem on convex means, to give a short non measure-theoretic proof of Lebesgue’s dominated convergence theorem for a sequence of continuous functions on a countably compact topological space, and to give a short proof of Banach’s criteria for the weak convergence of a sequence in the Banach space of all bounded, real functions on an abstract set. |
Mathematical Subject Classification
Primary: 46.06
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Milestones
Received: 19 November 1965
Published: 1 January 1967
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Authors |
| Stephen Simons | |
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