Theorems · Inductive type · real analysis
Real.HolderTriple
ℝ → ℝ → ℝ → Prop
Real numbers p q r : ℝ are said to be a Hölder triple if p and q are positive
and p⁻¹ + q⁻¹ = r⁻¹.
- Defined in
- Mathlib.Data.Real.ConjExponents
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
Cited by56
Results whose statement or proof uses this declaration.
- Real.HolderConjugateproof · cited by 78
- Real.HolderTriple.posstatement and proof · cited by 20
- Real.HolderTriple.pos'statement and proof · cited by 13
- Real.HolderTriple.nonnegstatement and proof · cited by 12
- Real.HolderTriple.inv_add_inv_eq_invstatement and proof · cited by 9
- Real.HolderTriple.ne_zerostatement and proof · cited by 9
- Real.HolderTriple.ltstatement and proof · cited by 8
- Real.HolderTriple.symmstatement and proof · cited by 7
- NNReal.HolderTriple.coestatement · cited by 6
- Real.HolderTriple.inv_posstatement and proof · cited by 5
- NNReal.summable_and_Lr_rpow_le_Lp_mul_Lq_tsumstatement and proof · cited by 4
- Real.HolderTriple.inv_nonnegstatement and proof · cited by 3