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I am looking for two reference incl. proofs showing

1) that a discrete Mixture of Gaussians can asymptotically approximate any (well behaved) continuous density

2) that a discrete Mixture of Bernoullies can asymptotically approximate any density over binary vectors.

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The answer to 1 is in http://a.co/d/jiJJM0y in either chapter 1 or 2, possibly in section 1.18.

There was a statement and reference to a proof that a Gaussian finite mixture was the PDF-version of an asymptotic approximation.

My personal copy of the book is at home, so I can't look it up at the moment.

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A proof of 2 is given in Dunson and Xing 2009: https://www.ncbi.nlm.nih.gov/pubmed/23606777

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