We introduce the notion of W-measurable sensitivity, which extends and
strictly implies canonical measurable sensitivity, the mesure-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
finite measure-preserving ergodic dynamical systems must be either W-measurably
sensitive, or isomorphic to an ergodic isometry on a compact metric space.