Theorems · Theorem · real analysis
ENNReal.rpow_add_le_mul_rpow_add_rpow
∀ (z₁ z₂ : ENNReal) {p : ℝ}, 1 ≤ p → (z₁ + z₂) ^ p ≤ 2 ^ (p - 1) * (z₁ ^ p + z₂ ^ p)Unweighted mean inequality, version for two elements of ℝ≥0∞ and real exponents.
- Defined in
- Mathlib.Analysis.MeanInequalitiesPow
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- one_divproof · cited by 624
- zero_le_oneproof · cited by 316
- two_ne_zeroproof · cited by 251
- ENNReal.rpow_oneproof · cited by 56
- ENNReal.inv_mul_cancelproof · cited by 33
- ENNReal.ofNat_ne_topproof · cited by 29
- ENNReal.add_halvesproof · cited by 24
Cited by3
Results whose statement or proof uses this declaration.
- ENNReal.rpow_add_le_mul_rpow_add_rpow'proof · cited by 1
- ENNReal.lintegral_rpow_add_lt_top_of_lintegral_rpow_lt_topproof · cited by 1
- ENNReal.lintegral_Lp_add_le_of_le_oneproof · cited by 1