Theorems · Theorem · probability
ProbabilityTheory.condCDF_eq_stieltjesOfMeasurableRat_unit_prod
∀ {α : Type u_1} {mα : MeasurableSpace α} (ρ : MeasureTheory.Measure (α × ℝ)) (a : α),
ProbabilityTheory.condCDF ρ a =
ProbabilityTheory.stieltjesOfMeasurableRat (fun p r => (ProbabilityTheory.preCDF ρ r p.2).toReal) ⋯ ((), a)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNReal.toRealstatement and proof · cited by 859
- Measurable.compstatement and proof · cited by 234
- StieltjesFunction.toFunproof · cited by 120
- measurable_sndstatement and proof · cited by 94
- StieltjesFunctionstatement and proof · cited by 85
- ProbabilityTheory.stieltjesOfMeasurableRatstatement and proof · cited by 22
- ProbabilityTheory.condCDFstatement · cited by 20
- ProbabilityTheory.preCDFstatement and proof · cited by 15
- ProbabilityTheory.measurable_preCDF'statement and proof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isCondKernelCDF_condCDFproof · cited by 5
- ProbabilityTheory.condCDF_ae_eqproof · cited by 1