Theorems · Theorem · real analysis
ENNReal.HolderConjugate.ne_top_iff_ne_one
∀ (p q : ENNReal) [p.HolderConjugate q], p ≠ ⊤ ↔ q ≠ 1
- Defined in
- Mathlib.Data.ENNReal.Holder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ENNReal.HolderConjugate
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement · cited by 9,680
- not_iff_notproof · cited by 159
- ENNReal.HolderConjugatestatement and proof · cited by 39
- ENNReal.HolderConjugate.eq_top_iff_eq_oneproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.HolderConjugate.lt_top_iff_one_ltproof · cited by 2