Sard’s theorem

Theorem.

Let $U$ be an open set in $R^m$, $V$ be an open set in $R^n$ and$f\mathrm{:}U\mathrm{\to }V$ be a $C^k$ function. If $k\mathrm{\ge }m\mathrm{/}n$, then the set ofcritical values of $f$ has $n$-dimensional measure zero.