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Theorems · Theorem · real analysis

ENNReal.rpow_one

∀ (x : ENNReal), x ^ 1 = x
Defined in
Mathlib.Analysis.SpecialFunctions.Pow.NNReal
Cited by
56 results in Mathlib
Foundations
Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

MeasureTheory.eLpNorm_one_eq_lintegral_enorm · cited by 16MeasureTheory.eLpNorm_one…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_rpowMeasureTheory.L1.norm_def · cited by 4L1.norm_defProbabilityTheory.evariance_lt_top · cited by 3ProbabilityTheory.evarian…ENNReal.rpow_add_le_mul_rpow_add_rpow · cited by 3ENNReal.rpow_add_le_mul_r…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…ProbabilityTheory.Kernel.eLpNorm_densityProcess_le · cited by 3Kernel.eLpNorm_densityPro…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_invReal · cited by 25697RealENNReal · cited by 9879ENNRealTop.top · cited by 9680Top.topNNReal · cited by 4310NNRealENNReal.ofNNReal · cited by 1279ENNReal.ofNNRealzero_lt_one · cited by 598zero_lt_onezero_le_one · cited by 316zero_le_oneLE.le.not_gt · cited by 189le.not_gtENNReal.recTopCoe · cited by 48ENNReal.recTopCoeNNReal.rpow_one · cited by 38NNReal.rpow_oneENNReal.rpow_oneCITED BYCITES

Cites10

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

Cited by56

Results whose statement or proof uses this declaration.