I found this statement about p-capacity used for the study of Sobolev functions: "$\mbox{Cap}_p$ is not a Borel measure. In fact, if $0< \mbox{Cap}_p(A) < \infty$, then $A$ is not $\mbox{Cap}_p$-measurable." I agree with the claim that $\mbox{Cap}_p$ is not a Borel (outer) measure, because balls are not $\mbox{Cap}_p$-measurable, but anyone know a proof of the second part? When I say "measure", i mean "outer measure".
2026-02-22 19:28:27.1771788507
$\mbox{Cap}_p$-measurability
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