Theorems · Theorem · probability

ProbabilityTheory.condExpKernel_ae_eq_condExp

∀ {Ω : Type u_1} {m : MeasurableSpace Ω} [mΩ : MeasurableSpace Ω] [inst : StandardBorelSpace Ω]
  {μ : MeasureTheory.Measure Ω} [inst_1 : MeasureTheory.IsFiniteMeasure μ],
  m ≤ mΩ →
    ∀ {s : Set Ω},
      MeasurableSet s → (fun ω => ((ProbabilityTheory.condExpKernel μ m) ω).real s) =ᵐ[μ] μ[s.indicator fun ω => 1 | m]

Defined in

Mathlib.Probability.Kernel.Condexp

Cited by

7 results in Mathlib

Foundations

Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceMeasureTheory.IsFiniteMeasure