Theorems · Definition · probability
ProbabilityTheory.cdf
MeasureTheory.Measure ℝ → StieltjesFunction ℝ
Cumulative distribution function of a real measure. The definition currently makes sense only
for probability measures. In that case, it satisfies cdf μ x = μ.real (Iic x) (see
ProbabilityTheory.cdf_eq_real).
- Defined in
- Mathlib.Probability.CDF
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- MeasureTheory.Measure.prodproof · cited by 353
- MeasureTheory.Measure.diracproof · cited by 210
- StieltjesFunctionstatement · cited by 85
- ProbabilityTheory.condCDFproof · cited by 20
Cited by19
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cdf_eq_realstatement and proof · cited by 5
- ProbabilityTheory.measure_cdfstatement and proof · cited by 2
- ProbabilityTheory.ofReal_cdfstatement · cited by 2
- ProbabilityTheory.tendsto_cdf_atBotstatement · cited by 2
- MeasureTheory.Measure.eq_of_cdfstatement and proof · cited by 1
- ProbabilityTheory.cdf_expMeasure_eq_lintegralstatement · cited by 1
- ProbabilityTheory.cdf_gammaMeasure_eq_integralstatement · cited by 1
- ProbabilityTheory.cdf_gammaMeasure_eq_lintegralstatement · cited by 1
- ProbabilityTheory.cdf_nonnegstatement · cited by 1
- ProbabilityTheory.unitInterval.cdf_eq_realstatement · cited by 0
- ProbabilityTheory.cdf_expMeasure_eqstatement · cited by 0
- ProbabilityTheory.monotone_cdfstatement · cited by 0