  The law of large numbers extends to random sets by employing Minkowski
addition. Above that, a central limit theorem is available for set-valued
random variables. The existing results use abstract isometries to describe
convergence of the sample mean process towards the limit, the expected value
set. These statements do not reveal the local geometry and the relations of the
sample mean and the expected value set, so these descriptions are not entirely
satisfactory in understanding the limiting behavior of the sample mean process.
This paper addresses and describes the fluctuations of the sample average mean
on the boundary of the expectation set.
