  In this paper, we introduce and study a notion of asymptotic expansion in
measure for measurable actions. This generalises expansion in measure and
provides a new perspective on the classical notion of strong ergodicity.
Moreover, we obtain structure theorems for asymptotically expanding actions,
showing that they admit exhaustions by domains of expansion. As an application,
we recover a recent result of Marrakchi, characterising strong ergodicity in
terms of local spectral gaps. We also show that homogeneous strongly ergodic
actions are always expanding in measure and establish a connection between
asymptotic expansion in measure and asymptotic expanders by means of
approximating spaces.
