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Mar 9, 2017 at 18:25 comment added Julian Newman I suspect it's not actually needed, but I used it to be able to get a compact set $K$ whose interior has measure arbitrarily close to $1$. With only $\sigma$-compactness, I might only be able to get $K$ itself to have measure arbitrarily close to $1$.
Mar 9, 2017 at 18:05 vote accept Eduardo
Mar 9, 2017 at 18:05 comment added Eduardo Sorry for the late response, thank you for the really nice the answer. Could you tell me where did you use the locally compact hypotesis?
Mar 7, 2017 at 6:40 history answered Julian Newman CC BY-SA 3.0