Real Analysis Exchange
- Real Anal. Exchange
- Volume 27, Number 1 (2001), 315-320.
Convergence of Metric Space-Valued BV Functions
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.
Real Anal. Exchange, Volume 27, Number 1 (2001), 315-320.
First available in Project Euclid: 6 June 2008
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Fleischer, Isidore; Porter, John E. Convergence of Metric Space-Valued BV Functions. Real Anal. Exchange 27 (2001), no. 1, 315--320. https://projecteuclid.org/euclid.rae/1212763970