Theorems · Theorem · real analysis
ENNReal.HolderConjugate.eq_top_iff_eq_one
∀ (p q : ENNReal) [p.HolderConjugate q], p = ⊤ ↔ q = 1
- Defined in
- Mathlib.Data.ENNReal.Holder
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 144 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.
Cites10
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 and proof · cited by 9,680
- inv_invproof · cited by 494
- inv_oneproof · cited by 301
- tsub_selfproof · cited by 154
- tsub_zeroproof · cited by 123
- ENNReal.HolderConjugatestatement and proof · cited by 39
- ENNReal.inv_zeroproof · cited by 37
- ENNReal.inv_topproof · cited by 36
- ENNReal.HolderConjugate.one_sub_invproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.HolderConjugate.ne_top_iff_ne_oneproof · cited by 1