Theorems · Theorem · functional analysis
PiLp.edist_eq_sum
∀ {ι : Type u_2} {β : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → EDist (β i)] {p : ENNReal},
0 < p.toReal → ∀ (f g : PiLp p β), edist f g = (∑ i, edist (f.ofLp i) (g.ofLp i) ^ p.toReal) ^ (1 / p.toReal)- 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.
Cites14
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
- Top.topproof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement · cited by 5,195
- Finset.univstatement · cited by 3,473
- LT.lt.ne'proof · cited by 1,417
- LT.lt.neproof · cited by 872
- ENNReal.toRealstatement and proof · cited by 859
- EDist.ediststatement · cited by 735
- WithLp.ofLpstatement · cited by 323
- PiLpstatement and proof · cited by 150
Cited by4
Results whose statement or proof uses this declaration.
- PiLp.edist_eq_of_L2proof · cited by 1
- PiLp.edist_eq_of_L1proof · cited by 0
- PiLp.edist_selfproof · cited by 0
- PiLp.edist_commproof · cited by 0