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Rectifiability of flat chains

Brian White
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Abstract

We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite mass and finite size is rectifiable. It also leads to a simple necessary and sufficient condition on the coefficient group in order for every finite-mass flat chain to be rectifiable.

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Brian White. 1999-07-01. Rectifiability of flat chains. https://arxiv.org/abs/math/9907209

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