Vol. 22, No. 3, 1967

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ISSN: 0030-8730
The iterated limit condition and sequential convergence

Stephen Simons

Vol. 22 (1967), No. 3, 505–513
Abstract

Let F be a family of functions from an abstract set X to a compact metric space W. This paper contains the following result: If F satisfies the iterated limit condition (see §1 below) then any function f0 : X W that is pointwise limit of elements of F can be expressed as the pointwise limit of a sequence extracted from F. Various generalizations are discussed, and applications are given to measure theory.

Mathematical Subject Classification
Primary: 54.22
Milestones
Received: 21 December 1965
Published: 1 September 1967
Authors
Stephen Simons