On general characterization of Young measures associated with Borel functions

We prove that the Young measure associated with a Borel function f is a probability distribution of the random variable f(U), where U has a uniform distribution on the domain of f. As an auxiliary result, the fact that Young measures associated with simple functions are weak* dense in the set of Young measures associated with measurable functions is proved. Finally some examples of specific applications of the main result are presented with comments.