Theorems · Theorem · convex and discrete geometry
Finset.centerMass_id_mem_convexHull
∀ {R : Type u_1} {E : Type u_3} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
[inst_3 : LinearOrder R] [IsStrictOrderedRing R] (t : Finset E) {w : E → R},
(∀ i ∈ t, 0 ≤ w i) → 0 < ∑ i ∈ t, w i → t.centerMass w id ∈ (convexHull R) ↑tA refinement of Finset.centerMass_mem_convexHull when the indexed family is a Finset of
the space.
- Defined in
- Mathlib.Analysis.Convex.Combination
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- SetLike.coestatement · cited by 8,199
- Fieldstatement and proof · cited by 7,404
- Finset.sumstatement and proof · cited by 5,195
- IsStrictOrderedRingstatement and proof · cited by 2,490
- ClosureOperatorstatement · cited by 371
- convexHullstatement · cited by 163
Cited by1
Results whose statement or proof uses this declaration.
- Finset.centroid_mem_convexHullproof · cited by 0