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Theorems · Theorem · real analysis

ENNReal.coe_rpow_of_nonneg

∀ (x : NNReal) {y : ℝ}, 0 ≤ y → ↑(x ^ y) = ↑x ^ y
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.NNReal
Cited by
34 results in Mathlib
Foundations
Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ENNReal.rpow_natCast · cited by 18ENNReal.rpow_natCastENNReal.strictMono_rpow_of_pos · cited by 7ENNReal.strictMono_rpow_o…HolderOnWith.dimH_image_le · cited by 3HolderOnWith.dimH_image_leMeasureTheory.exists_eLpNorm_indicator_le · cited by 3MeasureTheory.exists_eLpN…HolderOnWith.interpolate · cited by 3HolderOnWith.interpolateHolderOnWith.nndist_le_of_le · cited by 3HolderOnWith.nndist_le_of…MeasureTheory.Measure.hausdorffMeasure_smul₀ · cited by 3Measure.hausdorffMeasure_…HolderOnWith.comp · cited by 2HolderOnWith.compHolderOnWith.holderOnWith_zero_of_bounded · cited by 2HolderOnWith.holderOnWith…Real.enorm_rpow_of_nonneg · cited by 2Real.enorm_rpow_of_nonnegMeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul · cited by 2MeasureTheory.eLpNorm'_le…MeasureTheory.eLpNorm'_le_nnreal_smul_eLpNorm'_of_ae_le_mul' · cited by 2MeasureTheory.eLpNorm'_le…ENNReal.toNNReal_rpow · cited by 2ENNReal.toNNReal_rpowMeasureTheory.eLpNorm_smul_measure_of_ne_top' · cited by 2MeasureTheory.eLpNorm_smu…ENNReal.add_rpow_le_rpow_add · cited by 1ENNReal.add_rpow_le_rpow_…Real · cited by 25697RealENNReal · cited by 9879ENNRealNNReal · cited by 4310NNRealENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealne_of_gt · cited by 637ne_of_gtENNReal.rpow_zero · cited by 47ENNReal.rpow_zeroENNReal.zero_rpow_of_pos · cited by 36ENNReal.zero_rpow_of_posle_iff_eq_or_lt · cited by 20le_iff_eq_or_ltENNReal.coe_rpow_of_ne_zero · cited by 20ENNReal.coe_rpow_of_ne_ze…NNReal.rpow_zero · cited by 20NNReal.rpow_zeroNNReal.zero_rpow · cited by 16NNReal.zero_rpowENNReal.coe_rpow_of_nonnegCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by34

Results whose statement or proof uses this declaration.