Theorems · Theorem · real analysis
Real.holderConjugate_iff
∀ {p q : ℝ}, p.HolderConjugate q ↔ 1 < p ∧ p⁻¹ + q⁻¹ = 1- Defined in
- Mathlib.Data.Real.ConjExponents
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- zero_lt_oneproof · cited by 598
- LT.lt.transproof · cited by 370
- inv_oneproof · cited by 301
- sub_posproof · cited by 147
- inv_posproof · cited by 124
- Real.HolderConjugatestatement and proof · cited by 78
- inv_lt_one₀proof · cited by 9
- Real.HolderTriple.ltproof · cited by 8
- Real.HolderConjugate.inv_add_inv_eq_oneproof · cited by 6
- eq_sub_of_add_eq'proof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- NNReal.inner_le_weight_mul_Lpproof · cited by 2
- Real.holderConjugate_iff_eq_conjExponentproof · cited by 2
- Real.HolderConjugate.inv_one_sub_invproof · cited by 1
- ENNReal.lintegral_mul_norm_pow_leproof · cited by 1
- NNReal.holderConjugate_iffproof · cited by 1
- lp.summable_innerproof · cited by 1