Theorems · Theorem · functional analysis
EuclideanSpace.ball_zero_eq
∀ {n : Type u_7} [inst : Fintype n] (r : ℝ), 0 ≤ r → Metric.ball 0 r = {x | ∑ i, x.ofLp i ^ 2 < r ^ 2}- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 224 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Set.ofPredstatement and proof · cited by 6,101
- Norm.normproof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Set.extproof · cited by 2,266
- absproof · cited by 1,814
- Metric.ballstatement and proof · cited by 735
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanSpace.volume_ballproof · cited by 2