Theorems · Theorem · real analysis
ENNReal.young_inequality
∀ (a b : ENNReal) {p q : ℝ}, p.HolderConjugate q → a * b ≤ a ^ p / ENNReal.ofReal p + b ^ q / ENNReal.ofReal qYoung's inequality, ℝ≥0∞ version with real conjugate exponents.
- Defined in
- Mathlib.Analysis.MeanInequalities
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- ENNRealstatement and proof · cited by 9,879
- Top.topproof · cited by 9,680
- ENNReal.ofNNRealproof · cited by 1,279
- le_transproof · cited by 985
- ENNReal.ofRealstatement and proof · cited by 863
- div_eq_mul_invproof · cited by 715
- le_topproof · cited by 411
- le_of_eqproof · cited by 366
- Real.toNNRealproof · cited by 267
- ENNReal.toNNRealproof · cited by 165
- Real.HolderConjugatestatement and proof · cited by 78
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.lintegral_mul_le_one_of_lintegral_rpow_eq_oneproof · cited by 1