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.

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.

Can one give a reference to a result like this: If a sequence of convex functions f_n on R converges pointwise to a non-monotonic function f, then inf_R f_n converges to inf_R f? Thank you.

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.