Theorems · Theorem · convex and discrete geometry

ConvexOn.sup

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_5} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : AddCommMonoid β] [inst_4 : LinearOrder β] [IsOrderedAddMonoid β] [inst_6 : SMul 𝕜 E] [inst_7 : Module 𝕜 β]
  [PosSMulStrictMono 𝕜 β] {s : Set E} {f g : E → β}, ConvexOn 𝕜 s f → ConvexOn 𝕜 s g → ConvexOn 𝕜 s (f ⊔ g)

The pointwise maximum of convex functions is convex.

Defined in

Mathlib.Analysis.Convex.Function

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidLinearOrderIsOrderedAddMonoidSMulModulePosSMulStrictMono