# Level set

of a function $f$ on $\mathbf{R}^n$
The set of points in $\mathbf{R}^n$ on which $f= \text{const}$. If the function $f$ is given on a square $Q$ of the plane $\mathbf{R}^2$ and has partial derivatives there which also satisfy a Lipschitz condition, then for almost-all $c$ in the interval $\min f \le c \le \max f$ the level set $$M_c = \{ x \in Q \ :\ f(x) = c \}$$ consists of a finite number of regular curves (on them, $\mathrm{grad}\,f \ne 0$). Cf. Sard theorem.