EDB — 18Z

[18Z]Note:another vice versa of [183]↺↻.

Given \(I⊆ ℝ\) interval and \(f:I→ℝ∪\{ ∞\} \) convex and lower semicontinuous, there exist sequences \(a_ n,b_ n∈ℝ\) such that \(f(x)=\sup _ n (a_ n+b_ n x)\).