Theorems · Theorem · convex and discrete geometry

StrictConcaveOn.dual

∀ {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] [inst_5 : SMul 𝕜 E] [inst_6 : SMul 𝕜 β] {s : Set E} {f : E → β},
  StrictConcaveOn 𝕜 s f → StrictConvexOn 𝕜 s (⇑OrderDual.toDual ∘ f)

Defined in

Mathlib.Analysis.Convex.Function

Cited by

23 results in Mathlib

Foundations

Depth 15 from the axioms · uses Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidAddCommMonoidPartialOrderSMulSMul