Question: If {S1, S2, . . . , Sn} is a collection of convex subsets of a linear space X, their sum S1 + S2 +...........+

If {S1, S2, . . . , Sn} is a collection of convex subsets of a linear space X, their sum S1 + S2 +...........+ Sn is also a convex set.

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