Theorems · Theorem · functional analysis
PiLp.norm_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‖ = √(∑ i, ‖x.ofLp i‖ ^ 2)- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Nat.cast_oneproof · cited by 2,501
- Real.sqrtstatement and proof · cited by 545
- WithLp.ofLpstatement and proof · cited by 323
- PiLpstatement and proof · cited by 150
- Real.sqrt_eq_rpowproof · cited by 25
Cited by4
Results whose statement or proof uses this declaration.
- PiLp.nnnorm_eq_of_L2proof · cited by 5
- PiLp.dist_eq_of_L2proof · cited by 2
- Matrix.frobenius_norm_replicateRowproof · cited by 1
- Matrix.frobenius_norm_replicateColproof · cited by 1