Definition 15.1.8 (Vector Lattice).label Let $(E, \le)$ be an ordered vector space, then $E$ is a vector lattice if for any $x, y \in E$, $x \vee y = \sup\bracs{x, y}$ and $x \wedge y = \inf\bracs{x, y}$ exist.
Definition 15.1.8 (Vector Lattice).label Let $(E, \le)$ be an ordered vector space, then $E$ is a vector lattice if for any $x, y \in E$, $x \vee y = \sup\bracs{x, y}$ and $x \wedge y = \inf\bracs{x, y}$ exist.