Theorems · Theorem · convex and discrete geometry

QuasiconcaveOn.convex_gt

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_3} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommMonoid E]
  [inst_3 : LinearOrder β] [inst_4 : SMul 𝕜 E] {s : Set E} {f : E → β},
  QuasiconcaveOn 𝕜 s f → ∀ (r : β), Convex 𝕜 {x | x ∈ s ∧ r < f x}

Defined in

Mathlib.Analysis.Convex.Quasiconvex

Cited by

0 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Quot.sound

Assumes

SemiringPartialOrderAddCommMonoidLinearOrderSMul