If {S1, S2, . . . , Sn} is a collection of convex subsets of a linear

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If {S1, S2, . . . , Sn} is a collection of convex subsets of a linear space X, any linear combination a1S1 + a2S2 +............+ anSn, ai ∈ R is also a convex set.
Exercise 1.168 is a useful characterization of convex sets.
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