  A Daniell-Stone type characterization theorem for Aumann integrals of
set-valued measurable functions will be proven. It is assumed that the values
of these functions are closed convex upper sets, a structure that has been used
in some recent developments in set-valued variational analysis and set
optimization. It is shown that the Aumann integral of such a function is also a
closed convex upper set. The main theorem characterizes the conditions under
which a functional that maps from a certain collection of measurable set-valued
functions into the set of all closed convex upper sets can be written as the
Aumann integral with respect to some $\sigma$-finite measure. These conditions
include the analog of the conlinearity and monotone convergence properties of
the classical Daniell-Stone theorem for the Lebesgue integral, and three
geometric properties that are peculiar to the set-valued case as they are
redundant in the one-dimensional setting.
