  Lenz and Stollmann recently proved the existence of the integrated density of
states in the sense of uniform convergence of the distributions for certain
operators with aperiodic order. The goal of this paper is to establish a
relation between aperiodic order, uniform spectral convergence and the
continuous algebras invented by John von Neumann. We illustrate the technique
by proving the uniform spectral convergence for random Schodinger operators on
lattices with finite site probabilities, percolation Hamiltonians and for the
pattern-invariant operators of self-similar graphs.
