What is a $0$-sublevel set?

Question

I read the notes of S. Boyd, and am confused about the following:

$f_0(x)$ is quasiconvex. I am confused about the latter one particularly.
What does it mean?

Thanks!

Answer 1

The $0$-sublevel set of a function $g$ is the set $\{x: g(x)\le 0\}$.

Generally, the $t$-sublevel set of a function $g$ is the set $\{x: g(x)\le t\}$.

A function $g$ is called quasiconvex if for every $t$, the set $\{x: g(x)\le t\}$ is convex.