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Is there any result on the asymptotic behavior of the maximum of independent but non-identically distributed Gaussian random variables?

Something similar to the result by Gnedenko, (1947) that for a sequence of i.i.d. random variables $(x_{1},...x_{n})$ and $x_{max}=max(x_{1},...x_{n})$, we have $a_{n}(x_{max}-b_{n})$ converging in distribution to a random variable $G(x)$, where this distribution is Gumbel for i.i.d. Gaussian RVs.

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