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Theorems · Theorem · real analysis

ENNReal.rpow_mul

∀ (x : ENNReal) (y z : ℝ), x ^ (y * z) = (x ^ y) ^ z
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.NNReal
Cited by
33 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

IsSelfAdjoint.spectralRadius_eq_nnnorm · cited by 7IsSelfAdjoint.spectralRad…ENNReal.le_rpow_inv_iff · cited by 6ENNReal.le_rpow_inv_iffENNReal.rpow_inv_le_iff · cited by 5ENNReal.rpow_inv_le_iffENNReal.rpow_inv_rpow · cited by 5ENNReal.rpow_inv_rpowProbabilityTheory.evariance_lt_top · cited by 3ProbabilityTheory.evarian…HolderOnWith.interpolate · cited by 3HolderOnWith.interpolateMeasureTheory.mul_meas_ge_le_pow_eLpNorm · cited by 3MeasureTheory.mul_meas_ge…MeasureTheory.eLpNorm'_const · cited by 3MeasureTheory.eLpNorm'_co…MeasureTheory.eLpNorm'_le_eLpNormEssSup_mul_rpow_measure_univ · cited by 3MeasureTheory.eLpNorm'_le…MeasureTheory.Measure.hausdorffMeasure_zero_or_top · cited by 3Measure.hausdorffMeasure_…ENNReal.rpow_rpow_inv · cited by 3ENNReal.rpow_rpow_invHolderOnWith.comp · cited by 2HolderOnWith.compHolderOnWith.hausdorffMeasure_image_le · cited by 2HolderOnWith.hausdorffMea…MeasureTheory.lintegral_rpow_enorm_eq_rpow_eLpNorm' · cited by 2MeasureTheory.lintegral_r…ENNReal.lintegral_Lp_mul_le_Lq_mul_Lr · cited by 2ENNReal.lintegral_Lp_mul_…Real · cited by 25697RealENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topNNReal · cited by 4310NNRealMulZeroClass.mul_zero · cited by 2091MulZeroClass.mul_zeroMulZeroClass.zero_mul · cited by 1625MulZeroClass.zero_mulENNReal.ofNNReal · cited by 1279ENNReal.ofNNReallt_trichotomy · cited by 178lt_trichotomyENNReal.recTopCoe · cited by 48ENNReal.recTopCoeENNReal.rpow_zero · cited by 47ENNReal.rpow_zeroENNReal.zero_rpow_of_pos · cited by 36ENNReal.zero_rpow_of_posENNReal.top_rpow_of_pos · cited by 22ENNReal.top_rpow_of_posNNReal.rpow_mul · cited by 18NNReal.rpow_mulENNReal.top_rpow_of_neg · cited by 12ENNReal.top_rpow_of_negENNReal.one_rpow · cited by 12ENNReal.one_rpowENNReal.rpow_mulCITED BYCITES

Cites16

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

Cited by33

Results whose statement or proof uses this declaration.