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It seems that a mixture of Gaussians can approach any probability distribution, as the number of mixture components approaches infinity. Is this true? And if so, is it precise and correct to say that 'the Gaussian distribution is a dense subset of any distribution function'?

If not, how would you phrase this?

I have never seen anything about this in the literature about infinite mixtures of Gaussians.

Thanks very much!

Andrew

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# Gaussian distribution a dense subset of any distribution function?

It seems that a mixture of Gaussians can approach any probability distribution, as the number of mixture components approaches infinity. Is this true? And if so, is it precise and correct to say that 'the Gaussian distribution is a dense subset of any distribution function'?

If not, how would you phrase this?

I have never seen anything about this in the literature about infinite mixtures of Gaussians.

Thanks very much!

Andrew