The following noncompact analog of Choquet’s theorem is proved. Let
E
E
be a Banach space with the Radon-Nikodým property, let
C
C
be a separable, closed, bounded, convex subset of
E
E
, and let a be a point in
C
C
. Then there is a probability measure
μ
\mu
on the universally measurable sets in
C
C
such that
a
a
is the barycenter of
μ
\mu
and the set of extreme points of
C
C
has
μ
\mu
-measure 1.