Finitely additive measures and complementability of Lipschitz-free spaces

Abstract

We prove in particular that the Lipschitz-free space over a finitely-dimensional normed space is complemented in its bidual. For Euclidean spaces the norm of the respective projection is $1$. As a tool to obtain the main result we establish several facts on the structure of finitely additive measures on finitely-dimensional spaces.

24 pages; we corrected some misprints, reorganized a bit the introduction and added few comments (in particular one on the Leray projection)