-1
$\begingroup$

Suppose $\mathcal{F}$ is a Lipschitz function (Lipschitz constant $L$) space defined on $A$. $A$ is a bounded subset of $\mathbb{R^n}$. The $\mathcal{G}$ is an affine function space defined on $A$. The distance between $\mathcal{F}$ and $\mathcal{G}$ is defined as: $$\sup_{f\in \mathcal{F}} \inf_{g \in \mathcal G} ||f-g|| = \sup_{f\in \mathcal F} \inf_{g \in \mathcal G} \int_A (f(x) -g(x))^2 dx$$

Let me suppose $\forall x \in A,~||x|\leq M$.

$\endgroup$

closed as unclear what you're asking by YCor, user44191, Piotr Hajlasz, Stefan Waldmann, Davide Giraudo Mar 11 at 10:29

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ The statement is too general to be answered. If you have no further information about $A$ and $f$ you cannot compute the distance. $\endgroup$ – Piotr Hajlasz Mar 11 at 4:03