  In the Euclidean setting the celebrated Aleksandrov-Busemann-Feller theorem
states that convex functions are a.e. twice differentiable. In this paper we
prove that a similar result holds in the Heisenberg group, by showing that
every continuous H-convex function belongs to the class of functions whose
second order horizontal distributional derivatives are Radon measures. Together
with a recent result by Ambrosio and Magnani, this proves the existence a.e. of
second order horizontal derivatives for the class of continuous H-convex
functions in the Heisenberg group.
