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Let $u: \Omega\subset \mathbb{R}^N \to \mathbb{R}^M$ be a $BV$ function.

Is the box counting dimension of the graph of $u$ equal to $N$? How can we prove it?


The analogous question for the Hausdorff dimension was asked in Hausdorff dimension of the graph of a BV function (where related issues are also mentioned).

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