Given a submodular capacity space, we firstly obtain a quantitative estimate for the uniform convergence in the Choquet p-mean, 1\le p<\infty, of the multivariate stochastic Bernstein polynomials associated to a random function. Also, quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.

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 Gal,  Sorin G., Niculescu, Constantin P.