Theorems · Theorem · real analysis
ENNReal.mul_rpow_eq_ite
∀ (x y : ENNReal) (z : ℝ), (x * y) ^ z = if (x = 0 ∧ y = ⊤ ∨ x = ⊤ ∧ y = 0) ∧ z < 0 then ⊤ else x ^ z * y ^ z
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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.topstatement and proof · cited by 9,680
- NNRealproof · cited by 4,310
- mul_oneproof · cited by 3,885
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
- MulZeroClass.zero_mulproof · cited by 1,625
- ENNReal.ofNNRealproof · cited by 1,279
- eq_or_neproof · cited by 1,117
- mul_ne_zeroproof · cited by 178
Cited by5
Results whose statement or proof uses this declaration.
- ENNReal.mul_rpow_of_nonnegproof · cited by 23
- ENNReal.mul_rpow_of_ne_topproof · cited by 3
- MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul'proof · cited by 2
- MeasureTheory.eLpNorm'_le_mul_eLpNorm'_of_ae_le_mulproof · cited by 1
- ENNReal.mul_rpow_of_ne_zeroproof · cited by 1