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# Helly-Bray theorem

Let $F,F_{1},F_{2},\dots$ be distribution functions. If $F_{n}$ converges weakly to $F$, then

$\int_{\mathbb{R}}g(x)dF_{n}(x)\xrightarrow[n\rightarrow\infty]{}\int_{\mathbb{% R}}g(x)dF(x)$ |

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

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Theorem

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