FINITELY ADDITIVE MEASURES AND COMPLEMENTABILITY OF LIPSCHITZ-FREE SPACES

Abstract

We prove in particular that the Lipschitz-free space over a finite-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 finite-dimensional spaces.

Keywords

• Lipschitz-free space
• finitely-additive measure
• Banach space complemented in its bidual
• tangent spaces of a measure
• divergence of a measure