A chord-arc covering theorem in Hilbert space

Mathematics – Metric Geometry

Scientific paper

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Scientific paper

We prove that there exists $M>0$ such that for any closed rectifiable curve
$\Gamma$ in Hilbert space, almost every point in $\Gamma$ is contained in a
countable union of $M$ chord-arc curves whose total length is no more than $M$
times the length of $\Gamma$.

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