Definition:Convex Hull

Definition

Let $X$ be a vector space over $\R$.

Let $U \subseteq X$.

We define the convex hull of $U$, written $\map {\operatorname {conv} } U$ by:

$\ds \map {\operatorname {conv} } U = \set {\sum_{j \mathop = 1}^n \lambda_j u_j : n \in \N, \, u_j \in U \text { and } \lambda_j \in \R_{> 0} \text { for each } j, \, \sum_{j \mathop = 1}^n \lambda_j = 1}$

Also see

• Convex Hull is Smallest Convex Set containing Set
• Definition:Closed Convex Hull

• Results about convex hulls can be found here.

Sources

• 2020: James C. Robinson: Introduction to Functional Analysis ... (previous) ... (next) $21.5$: The Convex Hull