Theorems · Theorem · convex and discrete geometry

Finset.centerMass_mem_convexHull

∀ {R : Type u_1} {E : Type u_3} {ι : Type u_5} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
  {s : Set E} [inst_3 : LinearOrder R] [IsStrictOrderedRing R] (t : Finset ι) {w : ι → R},
  (∀ i ∈ t, 0 ≤ w i) → 0 < ∑ i ∈ t, w i → ∀ {z : ι → E}, (∀ i ∈ t, z i ∈ s) → t.centerMass w z ∈ (convexHull R) s

Defined in

Mathlib.Analysis.Convex.Combination

Cited by

11 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleLinearOrderIsStrictOrderedRing