Slutsky's theorem and the delta method

TheoremConvergence in distribution to a constant implies convergence in probability#✓fully proved

If the random variables X i on one probability space converge in distribution to the constant c, then they converge to c in probability.

theorem tendstoInMeasure_of_tendstoInDistribution_const [IsProbabilityMeasure P]
    [IsProbabilityMeasure P'] [PseudoMetricSpace E] [MeasurableSpace E] [BorelSpace E]
    {X : ι → Ω → E} {c : E} (h : TendstoInDistribution X l (fun _ : Ω' => c) (fun _ => P) P') :
    TendstoInMeasure P X l (fun _ => c)

Used by 1

Used byProduct of a distributionally convergent and a vanishing sequence

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