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How can i prove that a limit of a convex functions is convex. (a convergent sequence)

I knew that, If a sequence of convex continuous functions defined on a compact subset D of Rⁿ is convergent, then the limit function is convex on D. I do not know how to show this at all.

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    Dear sss, Welcome to math.SE. since you are a new user, we wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say what your thoughts on the problem are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level. Further, it would be better if you could typeset your problem so that it is easy for people to read. Kindly look here http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference for more details on typesetting.2012-10-30

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Hint: If $f_n\to f$ pointwise then $f_n(\lambda a+(1-\lambda) b)\to f(\lambda a+(1-\lambda) b)$ and $\lambda f_n(a)+(1-\lambda)f_n(b)\to \lambda f(a)+(1-\lambda)f(b).$

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    perhaps also indicates my laziness trying to prove something myself.2013-05-17