  We introduce the notion of W-measurable sensitivity, which extends and
strictly implies canonical measurable sensitivity, a measure- theoretic version
of sensitive dependence on initial conditions. This notion also implies
pairwise sensitivity with respect to a large class of metrics. We show that
nonsingular ergodic and conservative dynamical systems on standard spaces must
be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly
rigid isometry. In the finite measure-preserving case they are W-measurably
sensitive or measurably isomorphic to an ergodic isometry on a compact metric
space.
