  In 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for
elliptic operators in divergence form with bounded measurable coefficients. In
the Fermi lectures in 1998, Caffarelli stated a much simpler mean value theorem
for the same situation, but did not include the details of the proof. We show
all of the nontrivial details needed to prove the formula stated by Caffarelli,
and in the course of showing these details we establish some of the basic facts
about the obstacle problem for general elliptic divergence form operators, in
particular, we show a basic quadratic nondegeneracy property.
