# 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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