  We establish bounds on the density of states measure for Schr\"odinger
operators. These are deterministic results that do not require the existence of
the density of states measure, or, equivalently, of the integrated density of
states. The results are stated in terms of a "density of states outer-measure"
that always exists, and provides an upper bound for the density of states
measure when it exists. We prove log-H\"older continuity for this density of
states outer-measure in one, two, and three dimensions for Schr\"odinger
operators, and in any dimension for discrete Schr\"odinger operators.
