Richard J. Smith

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math.FA2024

A Choquet theory of Lipschitz-free spaces

Richard J. Smith

Let $(M, d)$ be a complete metric space and let $F (M)$ denote the Lipschitz-free space over $M$ . We develop a ``Choquet theory of Lipschitz-free spaces'' that draws from t…

math.FA2024

A solution to the extreme point problem and other applications of Choquet theory to Lipschitz-free spaces

Ramón J. Aliaga, Eva Pernecká, Richard J. Smith

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 point…