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Theo Johnson-Freyd
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convergence of the infima of convex functions

Can one give a reference to a result like this:

  • If a sequence of convex functions $f_{n}$ on $\mathbb{R}$ converges pointwise to a non-monotonic function $f$, then $\displaystyle\inf_{\mathbb{R}} f_n$ converges to $\displaystyle\inf_{\mathbb{R}} f$?

Thank you.

Iosif Pinelis
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