convex set proof
ProvethatK⊂RnisaconvexsetifandonlyifeveryconvexlinearcombinationofelementsinKalsobelongstoK.Proof:(⇒)weassumethatSconsistsm ...,Proof:LetKα}α∈Abeafamilyofconvexsets,andletK:=∩α∈AKα.Then,foranyx,y∈Kbydefinitionoftheintersectionofafamilyofsets,x,y∈...
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ProvethatK⊂RnisaconvexsetifandonlyifeveryconvexlinearcombinationofelementsinKalsobelongstoK.Proof:(⇒)weassumethatSconsistsm ...
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