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In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a broad class of densities on $\mathbb{R}^d$ can be approximated arbitrarily well in Kullback-Leibler (KL) divergence by elements in $\mathcal{P}$.
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