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April 6th, 2009, 12:31 PM   #1
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convex combination of closed and convex sets

Given:
is a vector space over the real numbers and are convex and closed sets in V.
is a closed and convex subset of .

My question : how to proof that is a closed convex set?

You can write as the image of the following bilinear function:
defined by , maybe it follows from properties of this function?

Thanks in advance for any help.
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