  We examine some of the properties of uniformly rigid transformations, and
analyze the compatibility of uniform rigidity and (measurable) weak mixing
along with some of their asymptotic convergence properties. We show that on
Cantor space, there does not exist a finite measure-preserving, totally
ergodic, uniformly rigid transformation. We briefly discuss general group
actions and show that (measurable) weak mixing and uniform rigidity can coexist
in a more general setting.
