Theorems · Theorem · probability
ProbabilityTheory.cdf_eq_real
∀ (μ : MeasureTheory.Measure ℝ) [MeasureTheory.IsProbabilityMeasure μ] (x : ℝ), ↑(ProbabilityTheory.cdf μ) x = μ.real (Set.Iic x)
- Defined in
- Mathlib.Probability.CDF
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- Set.Iicstatement and proof · cited by 1,111
- ENNReal.toRealproof · cited by 859
- MeasureTheory.Measure.realstatement · cited by 530
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- StieltjesFunction.toFunstatement and proof · cited by 120
- ENNReal.toReal_ofRealproof · cited by 82
- MeasureTheory.measureReal_defproof · cited by 68
- ProbabilityTheory.cdfstatement and proof · cited by 19
- ProbabilityTheory.ofReal_cdfproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cdf_gammaMeasure_eq_lintegralproof · cited by 1
- ProbabilityTheory.cdf_gammaMeasure_eq_integralproof · cited by 1
- ProbabilityTheory.unitInterval.cdf_eq_realproof · cited by 0
- ProbabilityTheory.cdf_paretoMeasure_eq_integralproof · cited by 0
- ProbabilityTheory.cdf_paretoMeasure_eq_lintegralproof · cited by 0