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We characterize sets of non-differentiability points of convex functions on ${ℝ}^n$. This completes (in ${ℝ}^n$) the result by Zajíček [2] which gives a characterization of the magnitude of these sets.

In [2] a delta convex function on ${ℝ}^2$ is constructed which is strictly differentiable at $0$ but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class $C^1\left({ℝ}^2\right)$ which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.