# Asymptotic behavior of the maximum of independent but non-identically distributed Gaussian random variables

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.