Theorems · Theorem · functional analysis
PiLp.iSup_edist_ne_top_aux
∀ {ι : Type u_5} [Finite ι] {α : ι → Type u_6} [inst : (i : ι) → PseudoMetricSpace (α i)] (f g : PiLp ⊤ α),
⨆ i, edist (f.ofLp i) (g.ofLp i) ≠ ⊤An auxiliary lemma used twice in the proof of PiLp.pseudoMetricAux below. Not intended for
use outside this file.
- Defined in
- Mathlib.Analysis.Normed.Lp.PiLp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FinitePseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- ENNRealstatement · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- iSupstatement · cited by 2,415
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.distproof · cited by 1,539
- ENNReal.ofNNRealproof · cited by 1,279
- LE.le.trans_ltproof · cited by 795
- EDist.ediststatement · cited by 735
- WithLp.ofLpstatement and proof · cited by 323
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