# fa.functional analysis – Does the space of Lipschitz functions have the Radon-Nikodym property?

Context.
Space of Lipschitz functions. Denote by $$Lip_0(D)$$ the space of all Lipschitz functions on a metric space $$D$$ vanishing at some base point $$e in D$$. The norm in $$Lip_0$$ is defined as follows
$$|f|_{Lip_0} := Lip(f),$$
where $$Lip(f)$$ denotes the Lipschitz constant of $$f$$.

Radon-Nikodym property (RNP). There are many equivalent definitions of the RNP, I will give two of them.
Definition 1. Let $$Sigma$$ be the $$sigma$$-algebra of subsets of a set $$Omega$$. A Banach space $$X$$ is said to have the RNP if for any measure $$mu colon Sigma to X$$ of bounded variation with values in $$X$$, and any finite positive scalar measure $$lambda colon Sigma to mathbb R$$ such that $$mu$$ is absolutely continuous w.r.t. $$lambda$$, there exists a $$lambda$$-Bochner integrable function $$f$$ such that $$mu(E) = int_E f ,dlambda$$ for all $$E in Sigma$$.
Theorem 1. A Banach space $$X$$ has the RNP if and only if every Lipschitz function $$mathbb R to X$$ is differentiable almost everywhere.

Question. Does the $$Lip_0$$ space have the Radon-Nikodym property?

I have tried the following sources, but wasn’t able to find an answer: Weaver, Lipschitz Algebras; Ryan, Introduction to Tensor Products of Banach Spaces; Diestel&Uhl, Vector Measures.

Any help will be much appreciated.