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June 28th, 2012, 03:06 AM   #1
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Convex set, convex function

Let's have a convex function .
We need to prove that is a convex set.

Any help would be appreciated.
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June 30th, 2012, 02:57 PM   #2
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Re: Convex set, convex function

Let and . Then and . We have:
. As is convex so
. Thereby , i.e. convex set.
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