Generalized symmetric polynomials and an approximate de Finetti representation (Q1780931)

A sequence of random variables \(X=(X_1,...,X_k)\) on a probability space \((\Omega, {\mathcal A}, {\mathbf P})\) with values in a measurable space \((M,{\mathcal B})\) is called exchangeable if its distribution \(P_X\), being a probability measure on the Cartesian power \((M^k ,{\mathcal B}^k),\) is symmetric under permutations of coordinates. In the paper for such symmetric probability measures the rate of approximation by mixtures of product measures is studied.