Theorems · Definition · functional analysis
lp.zeroBasis
{𝕜 : Type u_1} → {α : Type u_3} → [inst : NormedRing 𝕜] → Module.Basis α 𝕜 ↥(lp (fun x => 𝕜) 0)The basis for ℓ⁰(α, 𝕜) given by lp.single.
- Defined in
- Mathlib.Analysis.Normed.Lp.lpSpace
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- ENNRealstatement · cited by 9,879
- Finsuppproof · cited by 5,255
- AddSubgroupstatement · cited by 3,232
- Module.Basisstatement · cited by 1,477
- NormedRingstatement and proof · cited by 924
- PreLpstatement and proof · cited by 163
- lpstatement and proof · cited by 157
- Finsupp.ofSupportFiniteproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- lp.zeroBasis_applystatement · cited by 0
- lp.zeroBasis_repr_applystatement and proof · cited by 0