Theorems · Theorem · probability

ProbabilityTheory.setLIntegral_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, ENNReal.ofReal (↑(ProbabilityTheory.condCDF ρ a) x) ∂ρ.fst = ρ (s ×ˢ Set.Iic x)

Defined in: Mathlib.Probability.Kernel.Disintegration.CondCDF
Cited by: 0 results in Mathlib
Foundations: Depth 268 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.IsFiniteMeasure

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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 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
ENNRealstatement · cited by 9,879
MeasurableSetstatement and proof · cited by 3,075
SProd.sprodstatement · cited by 1,750
MeasureTheory.Measure.restrictstatement · cited by 1,646
MeasureTheory.lintegralstatement · cited by 1,152
Set.Iicstatement · cited by 1,111
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078

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