## Real Analysis Exchange

### Convergence of Metric Space-Valued BV Functions

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 27, Number 1 (2001), 315-320.

Dates
First available in Project Euclid: 6 June 2008

https://projecteuclid.org/euclid.rae/1212763970

Mathematical Reviews number (MathSciNet)
MR1887861

Zentralblatt MATH identifier
1035.26011

#### Citation

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

#### References

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