Is it true that the definition of [approximate differentiability presented here][1] of a function $f: \mathbb{R}^N \to \mathbb{R}$ is equivalent to the following one?
>$$\lim_{r \to 0} \rlap{-}\!\!\int_{B_r(x)} \min \left\{\frac{f(y)-f(x) - L(y-x)}{|y-x|},1 \right\} dy = 0$$
for some linear $L:\mathbb{R}^N \to \mathbb{R}$.



  [1]: https://www.encyclopediaofmath.org/index.php/Approximate_differentiability