Theorems · Theorem · probability

MeasureTheory.tendstoInDistribution_unique

∀ {ι : Type u_1} {E : Type u_2} {Ω' : Type u_3} {Ω'' : Type u_4} {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'] {m'' : MeasurableSpace Ω''} {μ'' : MeasureTheory.Measure Ω''}
  [inst_2 : MeasureTheory.IsProbabilityMeasure μ''] {mE : MeasurableSpace E} {l : Filter ι}
  [inst_3 : TopologicalSpace E] [HasOuterApproxClosed E] [inst_5 : BorelSpace E] (X : (i : ι) → Ω i → E) {Z : Ω' → E}
  {W : Ω'' → E} [l.NeBot],
  MeasureTheory.TendstoInDistribution X l Z μ μ' →
    MeasureTheory.TendstoInDistribution X l W μ μ'' → MeasureTheory.Measure.map Z μ' = MeasureTheory.Measure.map W μ''

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInDistribution

Cited by

0 results in Mathlib

Foundations

Depth 226 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.IsProbabilityMeasureMeasureTheory.IsProbabilityMeasureMeasureTheory.IsProbabilityMeasureTopologicalSpaceHasOuterApproxClosedBorelSpaceFilter.NeBot