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Topological balls with finite perimeter and finite floor touchstone retort

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Topological balls with finite perimeter and finite floor touchstone

Let $E subset mathbb{R}^d$ breathe homeomorphic to the $d$-dimensional ball, and occupy that $P(E)<+infty$ and $mathcal{H}^{d-1}(partial E) <+infty$. Here $P(E)$ is De Giorgi’s perimeter and $mathcal{H}^{okay}$ is the $okay$-dimensional Hausdorff touchstone.

Is it identified whether or not $partial E$ is $(d-1)$-rectifiable?

Alternatively, let $E$ breathe the graph of a steady responsibility of bounded distinction $f: mathbb{R}^d to mathbb{R}$. Is it identified whether or not $E$ is $(d-1)$-rectifiable?

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