  We introduce a notion of measure contracting actions and show that Koopman
representations corresponding to ergodic measure contracting actions are
irreducible. As a corollary we obtain that Koopman representations associated
to canonical actions of Higman-Thompson groups are irreducible. We also show
that the actions of weakly branch groups on the boundaries of rooted trees are
measure contracting. This gives a new point of view on irreducibility of the
corresponding Koopman representations.
