Theorems · Theorem · functional analysis
PiLp.nnnorm_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 222 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- NNRealstatement and proof · cited by 4,310
- Finset.univproof · cited by 3,473
- Factstatement and proof · cited by 2,726
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_reflproof · cited by 2,061
- Nat.cast_zeroproof · cited by 1,870
- LT.lt.ne'proof · cited by 1,417
Cited by4
Results whose statement or proof uses this declaration.
- PiLp.norm_singleproof · cited by 4
- PiLp.nndist_single_sameproof · cited by 4
- PiLp.nnnorm_toLp_singleproof · cited by 0
- EuclideanSpace.nnnorm_singleproof · cited by 0