Theorems · Theorem · functional analysis
PiLp.nndist_eq_iSup
∀ {ι : Type u_2} [inst : Fintype ι] {β : ι → Type u_5} [inst_1 : (i : ι) → PseudoMetricSpace (β i)] (x y : PiLp ⊤ β),
nndist x y = ⨆ i, nndist (x.ofLp i) (y.ofLp i)- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypePseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Fintypestatement and proof · cited by 7,736
- NNRealstatement · cited by 4,310
- iSupstatement · cited by 2,415
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- WithLp.ofLpstatement and proof · cited by 323
- NNDist.nndiststatement and proof · cited by 235
- NNReal.eqproof · cited by 201
- PiLpstatement and proof · cited by 150
- NNReal.coe_iSupproof · cited by 8
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