Theorems · Theorem · probability

MeasureTheory.TendstoInDistribution.congr

∀ {ι : Type u_1} {E : Type u_2} {Ω' : Type u_3} {Ω : ι → Type u_5} {m : (i : ι) → MeasurableSpace (Ω i)}
  {μ : (i : ι) → MeasureTheory.Measure (Ω i)} [inst : ∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)]
  {m' : MeasurableSpace Ω'} {μ' : MeasureTheory.Measure Ω'} [inst_1 : MeasureTheory.IsProbabilityMeasure μ']
  {mE : MeasurableSpace E} {X Y : (i : ι) → Ω i → E} {Z : Ω' → E} {l : Filter ι} [inst_2 : TopologicalSpace E]
  [inst_3 : OpensMeasurableSpace E] {T : Ω' → E},
  (∀ (i : ι), X i =ᵐ[μ i] Y i) →
    Z =ᵐ[μ'] T → MeasureTheory.TendstoInDistribution X l Z μ μ' → MeasureTheory.TendstoInDistribution Y l T μ μ'

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInDistribution

Cited by

0 results in Mathlib

Foundations

Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsProbabilityMeasureMeasureTheory.IsProbabilityMeasureTopologicalSpaceOpensMeasurableSpace