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2001/2002 Convergence of Metric Space-Valued BV Functions
Isidore Fleischer, John E. Porter
Real Anal. Exchange 27(1): 315-320 (2001/2002).


Chistyakov has proved ``Helly's selection theorem'' - a uniformly BV sequence has a pointwise convergent subsequence - for Banach-(resp. continuous, group-) valued functions from a real interval into a compact subset. We extend, dispensing with continuity, to arbitrary real subsets and lighten compactness of the range to pointwise precompactness (which answers one of his questions). In addition, we accomplish his selection more generally for complete metric-set-valued BV maps with closed graphs which are pointwise compact on dense subsets of their domains.


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Isidore Fleischer. John E. Porter. "Convergence of Metric Space-Valued BV Functions." Real Anal. Exchange 27 (1) 315 - 320, 2001/2002.


Published: 2001/2002
First available in Project Euclid: 6 June 2008

zbMATH: 1035.26011
MathSciNet: MR1887861

Primary: 26A45 , ‎54C60‎ , 54C65

Keywords: Bounded variation , pointwise precompact

Rights: Copyright © 2001 Michigan State University Press

Vol.27 • No. 1 • 2001/2002
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