Theorems · Theorem · real analysis

ConvexOn.inf_le_of_mem_convexHull

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_4} [inst : Field 𝕜] [inst_1 : LinearOrder 𝕜] [IsStrictOrderedRing 𝕜]
  [inst_3 : AddCommGroup E] [inst_4 : AddCommGroup β] [inst_5 : LinearOrder β] [IsOrderedAddMonoid β]
  [inst_7 : Module 𝕜 E] [inst_8 : Module 𝕜 β] [IsStrictOrderedModule 𝕜 β] {s : Set E} {f : E → β} {x : E}
  {t : Finset E}, ConcaveOn 𝕜 s f → ↑t ⊆ s → ∀ (hx : x ∈ (convexHull 𝕜) ↑t), t.inf' ⋯ f ≤ f x

Defined in

Mathlib.Analysis.Convex.Jensen

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldLinearOrderIsStrictOrderedRingAddCommGroupAddCommGroupLinearOrderIsOrderedAddMonoidModuleModuleIsStrictOrderedModule