Theorems · Theorem · functional analysis
PiLp.norm_eq_of_nat
∀ {ι : Type u_2} [inst : Fintype ι] {p : ENNReal} [Fact (1 ≤ p)] {β : ι → Type u_5}
[inst_2 : (i : ι) → SeminormedAddCommGroup (β i)] (n : ℕ),
p = ↑n → ∀ (f : PiLp p β), ‖f‖ = (∑ i, ‖f.ofLp i‖ ^ n) ^ (1 / ↑n)- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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 and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Factstatement and proof · cited by 2,726
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Finset.sum_congrproof · cited by 2,323
- ENNReal.toRealproof · cited by 859
- one_divproof · cited by 624
- Normproof · cited by 512
Cited by1
Results whose statement or proof uses this declaration.
- PiLp.norm_eq_of_L2proof · cited by 4