Theorems · Theorem · probability

MeasureTheory.TendstoInDistribution.forall_aemeasurable

∀ {ι : Type u_1} {E : Type u_2} {Ω' : Type u_3} {Ω : ι → Type u_5} {m : (i : ι) → MeasurableSpace (Ω i)}
  {m' : MeasurableSpace Ω'} {mE : MeasurableSpace E} [inst : TopologicalSpace E] [inst_1 : OpensMeasurableSpace E]
  {X : (i : ι) → Ω i → E} {l : Filter ι} {Z : Ω' → E} {μ : (i : ι) → MeasureTheory.Measure (Ω i)}
  [inst_2 : ∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)]
  {μ' : autoParam (MeasureTheory.Measure Ω') MeasureTheory.TendstoInDistribution._auto_1}
  [inst_3 : MeasureTheory.IsProbabilityMeasure μ'],
  MeasureTheory.TendstoInDistribution X l Z μ μ' → ∀ (i : ι), AEMeasurable (X i) (μ i)

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInDistribution

Cited by

5 results in Mathlib

Foundations

Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceOpensMeasurableSpaceMeasureTheory.IsProbabilityMeasureMeasureTheory.IsProbabilityMeasure