Theorems · Theorem · functional analysis
PiLp.norm_sq_eq_of_L2
∀ {ι : Type u_2} [inst : Fintype ι] (β : ι → Type u_5) [inst_1 : (i : ι) → SeminormedAddCommGroup (β i)] (x : PiLp 2 β),
‖x‖ ^ 2 = ∑ i, ‖x.ofLp i‖ ^ 2- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- NNRealproof · cited by 4,310
- Finset.univstatement and proof · cited by 3,473
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNReal.toRealproof · cited by 1,260
- NNNorm.nnnormproof · cited by 952
- WithLp.ofLpstatement and proof · cited by 323
- PiLpstatement and proof · cited by 150
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanSpace.norm_sq_eqproof · cited by 2
- PiLp.dist_sq_eq_of_L2proof · cited by 1