Does the boundary of the zero set of a smooth function $f : \mathbb{R}^n \to \mathbb{R}$ always have Lebesgue measure zero?
2026-03-27 11:46:37.1774611997
Boundary of zero set of smooth function
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The zero set of a smooth function can be any closed subset (a theorem of Whitney). So now you are asking if the boundary of a closed subset has always Legesgue measure $0$. Not always, as experimenting with some Cantor type subsets reveals.