In the theory of Sobolev space, we have the following chain rule:

- For a uniformly Lipschitz function $F : \mathbf{R}\to \mathbf{R}$ such that $F(0)=0$, and $u\in W^{1,1}(\mathbf{R}^n)$, then we have the following chain rule: $\partial_j F(u)=F'(u)\circ \partial_ju$.

But how to define the function $F'(u)$? It seems that we can't define $F'(u(.))$ a.e., and it may be not a measurable function.