  We prove that the integrated density of surface states of continuous or
discrete Anderson-type random Schroedinger operators is a measurable locally
integrable function rather than a signed measure or a distribution. This
generalize our recent results on the existence of the integrated density of
surface states in the continuous case and those of A. Chahrour in the discrete
case. The proof uses the new $L^p$-bound on the spectral shift function
recently obtained by Combes, Hislop, and Nakamura. Also we provide a simple
proof of their result on the Hoelder continuity of the integrated density of
bulk states.
