PlanetMath: Helly-Bray theorem

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Helly-Bray theorem

(Theorem)

Let $F,F_1,F_2,\dots$ be distribution functions. If converges weakly to , then

$\displaystyle \int_\mathbb{R} g(x)dF_n(x) \xrightarrow[n\rightarrow\infty]{} \int_\mathbb{R} g(x)dF(x)$

for each continuous bounded function $g:\mathbb{R}\rightarrow\mathbb{R}$ .

"Helly-Bray theorem" is owned by Koro.

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Cross-references: Riemann-Stieltjes integrals, integrals, bounded function, continuous, converges, distribution functions
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This is version 3 of Helly-Bray theorem, born on 2002-12-10, modified 2002-12-10.
Object id is 3710, canonical name is HellyBrayTheorem.
Accessed 3101 times total.

Classification:

60E05 (Probability theory and stochastic processes :: Distribution theory :: Distributions: general theory)

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