I thought about that, but the problem is that if it was the case, why should the classic Cauchy-Lipshitz theorem for $y'= f(t,y)$ be taught requiring "continuity in the independent variable and lipshitzianity in the other one"?

Thanks! Now that I think about it, there's another (smaller) issue I have. They say that whenever $b \in L^1 (0,T; W^{1, \infty})$, you have pointwise uniqueness for the ODE. Now, to me pointwise uniqueness means classical solution, but for that you'd need $b \in C([0,T];W^{1,\infty})$, don't you? I guess they mean they are pointwise unique in the sense that if you approximate $b$ with, say, smooth functions, the flows converge in $C([0,T]; \mathbb{R}^d)$

Yeah I guess I will. I'll just wait until September, just to let summer end

Federer, Simon, Evans-Gariepy, Maggi, Ambrosio-Fusco-Pallara, Morgan

Thanks to you all! I changed the word, didn't think it was THIS bad (I'm not a native english speaker)