Theorems · Theorem · probability
ProbabilityTheory.lintegral_condCDF
∀ {α : Type u_1} {mα : MeasurableSpace α} (ρ : MeasureTheory.Measure (α × ℝ)) [MeasureTheory.IsFiniteMeasure ρ] (x : ℝ),
∫⁻ (a : α), ENNReal.ofReal (↑(ProbabilityTheory.condCDF ρ a) x) ∂ρ.fst = ρ (Set.univ ×ˢ Set.Iic x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Set.univstatement · cited by 3,945
- SProd.sprodstatement · cited by 1,750
- MeasureTheory.lintegralstatement · cited by 1,152
- Set.Iicstatement · cited by 1,111
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- ENNReal.ofRealstatement · cited by 863
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.ofReal_cdfproof · cited by 2