theorem ERealFunction.quasiconvexOn_univ_of_convex {H : Type u} [AddCommMonoid H] [Module ℝ H] {f : H → EReal} (hf : IsConvex f) : QuasiconvexOn ℝ Set.univ f

Example 10.21: every convex extended-real-valued function on the whole space is quasiconvex on the whole space.