Theorems · Theorem · real analysis
ENNReal.mul_rpow_of_nonneg
∀ (x y : ENNReal) {z : ℝ}, 0 ≤ z → (x * y) ^ z = x ^ z * y ^ z- Cited by
- 23 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.
Cites5
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
- LE.le.not_gtproof · cited by 189
- ENNReal.mul_rpow_eq_iteproof · cited by 5
Cited by23
Results whose statement or proof uses this declaration.
- MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univproof · cited by 3
- ENNReal.rpow_add_le_mul_rpow_add_rpowproof · cited by 3
- HolderOnWith.interpolateproof · cited by 3
- MeasureTheory.eLpNorm'_constproof · cited by 3
- MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mulproof · cited by 2
- MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul'proof · cited by 2
- HolderOnWith.compproof · cited by 2
- ENNReal.lintegral_Lp_mul_le_Lq_mul_Lrproof · cited by 2
- HolderOnWith.hausdorffMeasure_image_leproof · cited by 2
- AntilipschitzWith.hausdorffMeasure_preimage_leproof · cited by 2
- MeasureTheory.eLpNorm'_le_mul_eLpNorm'_of_ae_le_mulproof · cited by 1