Vol. 40, No. 3, 1972

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A convergence theorem with boundary

Stephen Simons

Vol. 40 (1972), No. 3, 703–708
Abstract

This paper contains a bounded-convergence type theorem that depends on the fact that certain functions attain their suprema. Among the applications discussed are Rainwater’s theorem and two technical results, one used in the proof of the Choquet-Bishop-deLeeuw theorem and the other in the proof of Krein’s Theorem.

Mathematical Subject Classification
Primary: 46A05
Milestones
Received: 28 January 1971
Published: 1 March 1972
Authors
Stephen Simons