Definition (Level Set)

A level set of a real-valued function $f:\mathbb{R}^{n}\to \mathbb{R}$ of $n$ real variables is a set where the function takes on a given constant value $c$, that is: $$L_{c}(f)=\{(x_{1},…,x_{n})\in \mathbb{R}^{n}∣f(x_{1},…,x_{n})=c\}$$

Definition (Superlevel Set)

$$L_{c}^{+}(f)=\left\{(x_{1},\dots ,x_{n})\mid f(x_{1},\dots ,x_{n})\geq c\right\}$$is called a superlevel set of f (or, alternatively, an upper level set of f). And a strict superlevel set of f is $$\{(x_{1},…,x_{n})∣f(x_{1},…,x_{n})>c\}$$