Theorems · Theorem · probability
ProbabilityTheory.setIntegral_condCDF
∀ {α : Type u_1} {mα : MeasurableSpace α} (ρ : MeasureTheory.Measure (α × ℝ)) [MeasureTheory.IsFiniteMeasure ρ] (x : ℝ)
{s : Set α}, MeasurableSet s → ∫ (a : α) in s, ↑(ProbabilityTheory.condCDF ρ a) x ∂ρ.fst = ρ.real (s ×ˢ Set.Iic x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.integralstatement · cited by 1,779
- SProd.sprodstatement · cited by 1,750
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Set.Iicstatement · cited by 1,111
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.Measure.realstatement · cited by 530
- StieltjesFunction.toFunstatement · cited by 120
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