Theorems · Theorem · functional analysis
EuclideanSpace.basisFun_inner
∀ (ι : Type u_1) (𝕜 : Type u_3) [inst : RCLike 𝕜] [inst_1 : Fintype ι] (x : EuclideanSpace 𝕜 ι) (i : ι), inner 𝕜 ((EuclideanSpace.basisFun ι 𝕜) i) x = x.ofLp i
- Defined in
- Mathlib.Analysis.InnerProductSpace.PiL2
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 231 from the axioms · uses propext, Classical.choice, Quot.sound
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.coestatement · cited by 62,936
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- WithLp.ofLpstatement and proof · cited by 323
- EuclideanSpacestatement and proof · cited by 307
- OrthonormalBasisstatement · cited by 188
- EuclideanSpace.basisFunstatement and proof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.covarianceBilin_apply_basisFunproof · cited by 1
- ProbabilityTheory.covarianceBilin_apply_piproof · cited by 1
- EuclideanSpace.inner_basisFun_realproof · cited by 0
- ProbabilityTheory.HasGaussianLaw.iIndepFun_of_covariance_evalproof · cited by 0
- ProbabilityTheory.HasGaussianLaw.indepFun_of_covariance_evalproof · cited by 0