Theorems · Theorem · convex and discrete geometry

ConcaveOn.add

∀ {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 : PartialOrder β] [IsOrderedAddMonoid β] [inst_6 : SMul 𝕜 E]
  [inst_7 : DistribMulAction 𝕜 β] {s : Set E} {f g : E → β}, ConcaveOn 𝕜 s f → ConcaveOn 𝕜 s g → ConcaveOn 𝕜 s (f + g)

Defined in

Mathlib.Analysis.Convex.Function

Cited by

3 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidPartialOrderIsOrderedAddMonoidSMulDistribMulAction