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Results tagged with convexity
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user 99469
For questions involving the concept of convexity
5
votes
1
answer
437
views
Is there a Borel measurable $f:\mathbb{R}^d \to \mathbb{R}^d$ such that $f(x) \in \partial \...
Let $\varphi: \mathbb{R}^d \to \mathbb{R}$ be a convex function. The subdifferential of $f$ at $x$ is defined as
$$
\partial \varphi (x) := \{z \in \mathbb{R}^d : \varphi(y) \geq \varphi(x) + \langle …
- 825
4
votes
2
answers
245
views
Hausdorff dimension of the non-differentiability set a convex function
Let $X \subset \mathbb R^d$ be open, $f : X \to \mathbb R$ and
$$
E := \{x \in X : f \text{ is not Fréchet differentiable at }x\}.
$$
Then we have the following result which is
Theorem: If $X= \mathb …
- 825