Theorems · Theorem · convex and discrete geometry

ConcaveOn.comp_affineMap

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {β : Type u_5} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜]
  [inst_2 : AddCommGroup E] [inst_3 : AddCommGroup F] [inst_4 : AddCommMonoid β] [inst_5 : PartialOrder β]
  [inst_6 : Module 𝕜 E] [inst_7 : Module 𝕜 F] [inst_8 : SMul 𝕜 β] {f : F → β} (g : E →ᵃ[𝕜] F) {s : Set F},
  ConcaveOn 𝕜 s f → ConcaveOn 𝕜 (⇑g ⁻¹' s) (f ∘ ⇑g)

If a function is concave on s, it remains concave when precomposed by an affine map.

Defined in

Mathlib.Analysis.Convex.Function

Cited by

0 results in Mathlib

Foundations

Depth 50 from the axioms · uses propext, Quot.sound

Assumes

FieldLinearOrderAddCommGroupAddCommGroupAddCommMonoidPartialOrderModuleModuleSMul