Theorems · Theorem · real analysis

ConvexOn.pow

∀ {𝕜 : Type u_1} {E : Type u_2} {G : Type u_4} [inst : CommRing 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : CommRing E] [inst_4 : LinearOrder E] [IsStrictOrderedRing E] [inst_6 : AddCommGroup G] [inst_7 : Module 𝕜 G]
  [inst_8 : Module 𝕜 E] {s : Set G} [IsOrderedModule 𝕜 E] [IsScalarTower 𝕜 E E] [SMulCommClass 𝕜 E E] {f : G → E},
  ConvexOn 𝕜 s f → (∀ ⦃x : G⦄, x ∈ s → 0 ≤ f x) → ∀ (n : ℕ), ConvexOn 𝕜 s (f ^ n)

Defined in

Mathlib.Analysis.Convex.Mul

Cited by

3 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLinearOrderIsStrictOrderedRingCommRingLinearOrderIsStrictOrderedRingAddCommGroupModuleModuleIsOrderedModuleIsScalarTowerSMulCommClass