The metric approximation property and Lipschitz-free spaces over subsets of RNRN

We prove that for certain proper subsets MM of RNRN, N⩾1N⩾1, the Lipschitz-free space F(M)F(M) has the metric approximation property (MAP), with respect to any norm on RNRN. In particular, F(M)F(M) has the MAP whenever MM is a compact convex subset of a finite-dimensional space. This should be compared with a recent result of Godefroy and Ozawa, who showed that there exists a compact convex subset MM of a separable Banach space, for which F(M)F(M) fails the approximation property.