Young measure

Summary

A Young measure on a set $\Omega \subseteq \R^n$ is a measurable family $(\nu_x)_{x \in \Omega}$ of probability measures on $\R^m$. Young measures describe the limits of oscillating sequences of functions: $\nu_x$ is the distribution of the values that the functions take near $x$. They let one pass to the limit in nonlinear expressions $\varphi(u_k)$ when $u_k$ converges only weakly. They are a standard tool in the calculus of variations and in nonlinear partial differential equations.