Theorems · Theorem · real analysis
ENNReal.rpow_le_rpow
∀ {x y : ENNReal} {z : ℝ}, x ≤ y → 0 ≤ z → x ^ z ≤ y ^ z- Cited by
- 29 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.
Cites3
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
- ENNReal.monotone_rpow_of_nonnegproof · cited by 3
Cited by29
Results whose statement or proof uses this declaration.
- HolderOnWith.edist_le_of_leproof · cited by 4
- MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univproof · cited by 3
- MeasureTheory.SimpleFunc.tendsto_approxOn_Lp_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm'_mono_enorm_aeproof · cited by 3
- MeasureTheory.exists_eLpNorm_indicator_leproof · cited by 3
- HolderOnWith.interpolateproof · cited by 3
- MeasureTheory.mul_meas_ge_le_pow_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm_le_eLpNorm_top_mul_eLpNormproof · cited by 3
- MeasureTheory.eLpNorm'_le_eLpNorm'_mul_eLpNorm'proof · cited by 2
- MeasureTheory.pow_mul_meas_ge_le_eLpNormproof · cited by 2
- ENNReal.lintegral_Lp_mul_le_Lq_mul_Lrproof · cited by 2
- HolderOnWith.hausdorffMeasure_image_leproof · cited by 2