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

We prove that for certain proper subsets M of R-N, N >= 1, the Lipschitz-free space F(M) has the metric approximation property (MAP), with respect to any norm on R-N. In particular, F(M) has the MAP whenever M 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 M of a separable Banach space, for which F(M) fails the approximation property. (C) 2015 Elsevier Inc. All rights reserved.