Theorems · Theorem · approximation theory
bernsteinApproximation.apply
∀ {E : Type u_1} [inst : AddCommGroup E] [inst_1 : TopologicalSpace E] [inst_2 : IsTopologicalAddGroup E]
[inst_3 : Module ℝ E] [inst_4 : ContinuousSMul ℝ E] (n : ℕ) (f : C(↑unitInterval, E)) (x : ↑unitInterval),
(bernsteinApproximation n f) x = ∑ k, (bernstein n ↑k) x • f (bernstein.z k)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.Elemstatement and proof · cited by 7,166
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- ContinuousMapstatement and proof · cited by 2,491
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- ContinuousSMulstatement and proof · cited by 1,016
Cited by3
Results whose statement or proof uses this declaration.
- bernsteinApproximation_uniformproof · cited by 1
- bernsteinApproximation.apply_oneproof · cited by 0
- bernsteinApproximation.apply_zeroproof · cited by 0