Theorems · Theorem · functional analysis
PiLp.nnnorm_eq_of_L2
∀ {ι : Type u_2} {β : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → SeminormedAddCommGroup (β i)] (x : PiLp 2 β),
‖x‖₊ = NNReal.sqrt (∑ i, ‖x.ofLp i‖₊ ^ 2)- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Norm.normproof · cited by 5,413
- Finset.sumstatement · cited by 5,195
- NNRealstatement · cited by 4,310
- Finset.univstatement and proof · cited by 3,473
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement and proof · cited by 952
- OrderIsostatement · cited by 874
- Real.sqrtproof · cited by 545
- WithLp.ofLpstatement and proof · cited by 323
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.frobenius_nnnorm_defproof · cited by 5
- Matrix.frobenius_nnnorm_diagonalproof · cited by 2
- PiLp.norm_sq_eq_of_L2proof · cited by 2
- EuclideanSpace.nnnorm_eqproof · cited by 1
- Matrix.frobenius_nnnorm_mulproof · cited by 1