Theorems · Inductive type · probability

MeasureTheory.TendstoInDistribution

{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] →
                [OpensMeasurableSpace E] →
                  ((i : ι) → Ω i → E) →
                    Filter ι →
                      (Ω' → E) →
                        (μ : (i : ι) → MeasureTheory.Measure (Ω i)) →
                          [∀ (i : ι), MeasureTheory.IsProbabilityMeasure (μ i)] →
                            (μ' : autoParam (MeasureTheory.Measure Ω') MeasureTheory.TendstoInDistribution._auto_1) →
                              [MeasureTheory.IsProbabilityMeasure μ'] → Prop

Convergence in distribution of random variables. This is the weak convergence of the laws of the random variables: Tendsto in the ProbabilityMeasure type.

Defined in

Mathlib.MeasureTheory.Function.ConvergenceInDistribution

Cited by

19 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

TopologicalSpaceOpensMeasurableSpaceMeasureTheory.IsProbabilityMeasureMeasureTheory.IsProbabilityMeasure