Theorems · Theorem · measure theory

MeasureTheory.condLExp_def

∀ {Ω : Type u_2} {mΩ₀ : MeasurableSpace Ω} (mΩ : MeasurableSpace Ω) (P : MeasureTheory.Measure Ω) (X : Ω → ENNReal),
  P⁻[X | mΩ] =
    if hm : mΩ ≤ mΩ₀ then
      if MeasureTheory.SigmaFinite (P.trim hm) then
        if Measurable X then X else ((P.withDensity X).trim hm).rnDeriv (P.trim hm)
      else 0
    else 0

Defined in

Mathlib.MeasureTheory.Function.ConditionalLExpectation

Cited by

4 results in Mathlib

Foundations

Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound