Theorems · Theorem · probability

MeasureTheory.TendstoInDistribution.tendsto

∀ {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'] (self : MeasureTheory.TendstoInDistribution X l Z μ μ'),
  Filter.Tendsto (fun n => ⟨MeasureTheory.Measure.map (X n) (μ n), ⋯⟩) l (nhds ⟨MeasureTheory.Measure.map Z μ', ⋯⟩)

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInDistribution

Cited by

5 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceOpensMeasurableSpaceMeasureTheory.IsProbabilityMeasureMeasureTheory.IsProbabilityMeasure