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Theorems · Theorem · measure theory

MeasureTheory.measureReal_def

∀ {α : Type u_6} {m : MeasurableSpace α} (μ : MeasureTheory.Measure α) (s : Set α), μ.real s = (μ s).toReal
Defined in
Mathlib.MeasureTheory.Measure.MeasureSpaceDef
Cited by
68 results in Mathlib
Foundations
Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

MeasureTheory.average_eq · cited by 10MeasureTheory.average_eqMeasureTheory.DominatedFinMeasAdditive.eq_zero_of_measure_zero · cited by 9DominatedFinMeasAdditive.…MeasureTheory.JordanDecomposition.toSignedMeasure_injective · cited by 6JordanDecomposition.toSig…MeasureTheory.toReal_rnDeriv_map · cited by 5MeasureTheory.toReal_rnDe…ProbabilityTheory.cdf_eq_real · cited by 5ProbabilityTheory.cdf_eq_…ProbabilityTheory.Kernel.setIntegral_densityProcess · cited by 4Kernel.setIntegral_densit…MeasureTheory.norm_indicatorConstLp · cited by 4MeasureTheory.norm_indica…MeasureTheory.Measure.real_def · cited by 4Measure.real_defMeasureTheory.weightedSMul_null · cited by 3MeasureTheory.weightedSMu…BoxIntegral.Box.volume_apply · cited by 3Box.volume_applyMeasureTheory.condExp_bot' · cited by 3MeasureTheory.condExp_bot'MeasureTheory.integral_countable · cited by 3MeasureTheory.integral_co…MeasureTheory.toReal_laverage · cited by 3MeasureTheory.toReal_lave…ProbabilityTheory.Kernel.setIntegral_density · cited by 2Kernel.setIntegral_densityProbabilityTheory.Kernel.setLIntegral_density · cited by 2Kernel.setLIntegral_densi…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetReal · cited by 25697RealMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealENNReal.toReal · cited by 859ENNReal.toRealMeasureTheory.Measure.real · cited by 530Measure.realMeasureTheory.measureReal_defCITED BYCITES

Cites8

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

Cited by68

Results whose statement or proof uses this declaration.