Theorems · Theorem · functional analysis
PiLp.edist_eq_of_L2
∀ {ι : Type u_2} {β : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → SeminormedAddCommGroup (β i)]
(x y : PiLp 2 β), edist x y = (∑ i, edist (x.ofLp i) (y.ofLp i) ^ 2) ^ (1 / 2)- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 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 · cited by 9,879
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Finset.sum_congrproof · cited by 2,323
- EDist.ediststatement and proof · cited by 735
- one_divproof · cited by 624
- WithLp.ofLpstatement and proof · cited by 323
- PiLpstatement and proof · cited by 150
- ENNReal.toReal_ofNatproof · cited by 23
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanSpace.edist_eqproof · cited by 0