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


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

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  • $\begingroup$ 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