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