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- Jan 26, 2012

- 995

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**Problem**: The

**convex hull**of a subset $A$ in a vector space $V$ is the set of all convex combinations of vectors from $A$, that is,\[t_1x_1+t_2x_2+\cdots+t_nx_n,\]

where $t_i\in[0,1]$ and $\sum_{i=1}^n t_i=1$, $x_1,x_2,\ldots,x_n\in A$ and $n\in\mathbb{N}$ any natural number. Prove that the convex hull of $A$ is convex and that it is the intersection of all convex sets that contain $A$.

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