Definition:Lower Level Set

Definition
Let $f:S\to\R\cup\left\{-\infty,\infty\right\}$ be an extended-real-valued function and let $\alpha\in\R$.

The $\alpha$-lower level set of $f$ is the set:


 * $\operatorname{lev}_{\leq\alpha}f := \left\{ x\in S,\ f(x)\leq \alpha\right\}$