# Box counting dimension of the graph of a BV function

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).