General Regions in 2D

Definition: General Region in ${\mathbb{R}}^2$

A general region of in ${\mathbb{R}}^2$ is a subset $D\subseteq {\mathbb{R}}^2$ which can be described in one of the following ways for two real numbers $a,b$ and two continuous real functions $l,u:[a;b]\to \mathbb{R}$:

• Type I: $D=\{(x,y)\mid a\le x\le b,l(x)\le y\le u(x)\}$
• Type II: $D=\{(x,y)\mid l(y)\le x\le u(y),a\le y\le b\}$