Let $V$ be some vector space over $\Bbb{R}$ Let $X$ be some set of elements of $V$ Then a convex combination of elements from $X$ is a linear combination of the form $$\lambda_1 x_1 + \lambda_2 x_2 + \cdots + \lambda_n x_n$$ for some $n > 0$ where each $x_i \in X$ each $\lambda_i \ge 0$ and $\sum_i \lambda_i = 1$

Let ${\rm co}(X)$ be the set of all convex combinations from $X$ We call ${\rm co}(X)$ the convex hull, or convex envelope, or convex closure of $X$ It is a convex set, and is the smallest convex set which contains $X$ A set $X$ is convex if and only if $X = {\rm co}(X)$