Theorems · Theorem · convex and discrete geometry

ConvexOn.smul

∀ {𝕜 : Type u_1} {E : Type u_2} {β : Type u_5} [inst : CommSemiring 𝕜] [inst_1 : PartialOrder 𝕜]
  [inst_2 : AddCommMonoid E] [inst_3 : AddCommMonoid β] [inst_4 : PartialOrder β] [inst_5 : SMul 𝕜 E]
  [inst_6 : Module 𝕜 β] [PosSMulMono 𝕜 β] {s : Set E} {f : E → β} {c : 𝕜},
  0 ≤ c → ConvexOn 𝕜 s f → ConvexOn 𝕜 s fun x => c • f x

Defined in

Mathlib.Analysis.Convex.Function

Cited by

4 results in Mathlib

Foundations

Depth 15 from the axioms · uses no axioms

Assumes

CommSemiringPartialOrderAddCommMonoidAddCommMonoidPartialOrderSMulModulePosSMulMono