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We prove that the family of measured dynamical systems which can be realisedas uniquely ergodic minimal homeomorphisms on a given manifold (of dimension atleast two) is stable under measured extension. As a corollary, any ergodicsystem with an irrational eigenvalue is isomorphic to a uniquely ergodicminimal homeomorphism on the two-torus. The proof uses the followingimprovement of Weiss relative version of Jewett-Krieger theorem: any extensionbetween two ergodic systems is isomorphic to a skew-product on Cantor sets.

Realisation of measured dynamics as uniquely ergodic minimal homeomorphisms on manifolds