Young measure, superposition and transport Patrick Bernard 28A3349J4537J50Young measuresminimizationtonelli theoremMather measuresclosed measurestransport We discuss a space of Young measures in connection with some variational problems. We use it to present a proof of the Theorem of Tonelli on the existence of minimizing curves. We generalize a recent result of Ambrosio, Gigli and Savar\'e on the decomposition of the weak solutions of the transport equation. We also prove, in the context of Mather theory, the equality between Closed measures and Holonomic measures. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3163 10.1512/iumj.2008.57.3163 en Indiana Univ. Math. J. 57 (2008) 247 - 276 state-of-the-art mathematics http://iumj.org/access/