Theorems · Theorem · functional analysis
PiLp.norm_single
∀ (p : ENNReal) {ι : Type u_2} (β : ι → Type u_4) [hp : Fact (1 ≤ p)] [inst : Fintype ι]
[inst_1 : (i : ι) → SeminormedAddCommGroup (β i)] [inst_2 : DecidableEq ι] (i : ι) (b : β i),
‖PiLp.single p i b‖ = ‖b‖- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement · cited by 5,413
- Factstatement and proof · cited by 2,726
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNReal.toRealproof · cited by 1,260
- PiLpstatement · cited by 150
- PiLp.singlestatement · cited by 24
- PiLp.nnnorm_singleproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Matrix.l2_opNorm_diagonalproof · cited by 1
- PiLp.norm_toLp_singleproof · cited by 0
- Matrix.permMatrix_l2_opNorm_eqproof · cited by 0
- EuclideanSpace.norm_singleproof · cited by 0