2024/12/05 by Aliaga, Ramón J., Pernecká, Eva, Smith, Richard J. · 1 citation
#46B04 #46B20 #46E15 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2412.04312
We prove that every element of a Lipschitz-free space admits an expression as a convex series of elements with compact support. As a consequence, we conclude that all extreme points of the unit ball of Lipschitz-free spaces are elementary molecules, solving a long-standing problem. We also deduce that all elements of a Lipschitz-free space with the Radon-Nikodým property can be expressed as convex integrals of molecules. Our results are based on a recent theory of integral representation for functionals on Lipschitz spaces which draws on classical Choquet theory, due to the third named author.