  We show that, given a metric space $(Y,d)$ of curvature bounded from above in
the sense of Alexandrov, and a positive Radon measure $\mu$ on $Y$ giving
finite mass to bounded sets, the resulting metric measure space $(Y,d,\mu)$ is
infinitesimally Hilbertian, i.e. the Sobolev space $W^{1,2}(Y,d,\mu)$ is a
Hilbert space.
  The result is obtained by constructing an isometric embedding of the
`abstract and analytical' space of derivations into the `concrete and
geometrical' bundle whose fibre at $x\in Y$ is the tangent cone at $x$ of $Y$.
The conclusion then follows from the fact that for every $x\in Y$ such a cone
is a CAT(0)-space and, as such, has a Hilbert-like structure.
