  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.
