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Let X = (X1, X2, …) be a sequence of random variables with values in a standard space (S, B). Suppose(FORMULA PRESENT)where θ > 0 is a constant, ν a probability measure on B, and K a random probability measure on B. Then, X is exchangeable whenever K is a regular conditional distribution for ν given any sub-σ-field of B. Under this assumption, X enjoys all the main properties of classical Dirichlet sequences, including Sethuraman’s representa-tion, conjugacy property, and convergence in total variation of predictive distributions. If μ is the weak limit of the empirical measures, conditions for μ to be a.s. discrete, or a.s. non-atomic, or μ ≪ ν a.s., are provided. Two CLT’s are proved as well. The first deals with stable convergence while the second concerns total variation distance.

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Berti, P., Dreassi, E., Leisen, F., Pratelli, L., & Rigo, P. (2023). Kernel based Dirichlet sequences. *Bernoulli*, *29*(2), 1321–1342. https://doi.org/10.3150/22-BEJ1500

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