Theorems · Theorem · probability
ProbabilityTheory.integral_preCDF_fst
∀ {α : Type u_1} {mα : MeasurableSpace α} (ρ : MeasureTheory.Measure (α × ℝ)) (r : ℚ) [MeasureTheory.IsFiniteMeasure ρ],
∫ (x : α), (ProbabilityTheory.preCDF ρ r x).toReal ∂ρ.fst = (ρ.IicSnd ↑r).real Set.univ- Cited by
- 1 results in Mathlib
- Foundations
- Depth 256 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
- Set.univstatement and proof · cited by 3,945
- MeasureTheory.integralstatement · cited by 1,779
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- ENNReal.toRealstatement · cited by 859
- MeasureTheory.Measure.realstatement and proof · cited by 530
- MeasurableSet.univproof · cited by 178
- MeasureTheory.Measure.fststatement · cited by 70
- MeasureTheory.setIntegral_univproof · cited by 25
- MeasureTheory.Measure.IicSndstatement and proof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.isRatCondKernelCDFAux_preCDFproof · cited by 1