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Theorems · Theorem · functional analysis

PiLp.edist_eq_card

∀ {ι : Type u_2} {β : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → EDist (β i)] (f g : PiLp 0 β),
  edist f g = ↑⋯.toFinset.card
Defined in
Mathlib.Analysis.Normed.Lp.PiLp
Cited by
2 results in Mathlib
Foundations
Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeEDist
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

PiLp.edist_self · cited by 0PiLp.edist_selfPiLp.edist_comm · cited by 0PiLp.edist_commSet · cited by 53352SetENNReal · cited by 9879ENNRealFintype · cited by 7736FintypeSet.ofPred · cited by 6101Set.ofPredFinset.card · cited by 2327Finset.cardEDist.edist · cited by 735EDist.edistSet.Finite.toFinset · cited by 351Finite.toFinsetWithLp.ofLp · cited by 323WithLp.ofLpSet.toFinite · cited by 174Set.toFinitePiLp · cited by 150PiLpEDist · cited by 91EDistPiLp.edist_eq_cardCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.