Definition 9.1.1 (Convex). Let $E$ be a vector space over $K \in \RC$, then $A \subset E$ is convex if for any $x, y \in A$, $\bracs{\lambda x + (1 - \lambda) y| \lambda \in [0, 1]}\subset A$.
Definition 9.1.1 (Convex). Let $E$ be a vector space over $K \in \RC$, then $A \subset E$ is convex if for any $x, y \in A$, $\bracs{\lambda x + (1 - \lambda) y| \lambda \in [0, 1]}\subset A$.