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- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- ENNReal.toRealstatement · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
Cited by68
Results whose statement or proof uses this declaration.
- MeasureTheory.average_eqproof · cited by 10
- MeasureTheory.DominatedFinMeasAdditive.eq_zero_of_measure_zeroproof · cited by 9
- MeasureTheory.JordanDecomposition.toSignedMeasure_injectiveproof · cited by 6
- MeasureTheory.toReal_rnDeriv_mapproof · cited by 5
- ProbabilityTheory.cdf_eq_realproof · cited by 5
- ProbabilityTheory.Kernel.setIntegral_densityProcessproof · cited by 4
- MeasureTheory.norm_indicatorConstLpproof · cited by 4
- MeasureTheory.Measure.real_defproof · cited by 4
- MeasureTheory.weightedSMul_nullproof · cited by 3
- BoxIntegral.Box.volume_applyproof · cited by 3
- MeasureTheory.condExp_bot'proof · cited by 3
- MeasureTheory.integral_countableproof · cited by 3