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Dirichlet process mixtures, obtained by convolving the law of a Dirichlet process with a suitable kernel, are popular methods for density estimation. Due to the almost sure discreteness of the mixing measure, they automatically provide a latent clustering which is often of great interest for applied researchers. However, despite its relevance, little is known about the posterior properties of clustering, even with a large sample. We contribute by considering a simple data generating mechanism and showing the asymptotic properties of the maximum a posteriori clustering with Gaussian kernel.