  We define a way of approximating actions on measure spaces using finite
graphs; we then show that in quite general settings these graphs form a family
of expanders if and only if the action is expanding in measure. This provides a
somewhat unified approach to construct expanders. We also show that the graphs
we obtain are uniformly quasi-isometric to the level sets of warped cones. This
way we can also prove non-embeddability results for the latter and restate an
old conjecture of Gamburd-Jakobson-Sarnak.
