I've been looking at this for a proof of Rademacher's theorem on differentiability of Lipschitz functions. At the start of p. 8, in the proof of the theorem, the pdf sets:
$$A=\int_kA_k.$$
But that's no ordinary integral. First of all because $k$ is integer (I think), so at the very least we would need a measure on $\mathbb{N}$. But in any case, the biggest problem is that $A_k$ is a set for all $k$. So what does this integral mean?
@Jonas suggests it might be a misprint for $\cap$.
I thought maybe the author of the pdf thought, for a moment, that "int" stood for "intersection", and didn't see the error before uploading.
I don't think denoting an intersection as an integral is really used much as a notation, is it?
It seems it might really be an intersection. The offending part is:
If $A$ were an intersection, the "and so" would be fine. It would hold for any strange union of intersections, I should think. But the following bit uses $df$ for $x\in A$, and since $A_k$ is where $D_{v_k}f$ exists, having chosen $v_k$ as a countable dense subset of the sphere, I certainly need an intersection to have a differential, right?