Approximation of Random Functions by Random Polynomials in the Framework of Choquet's Theory of Integration
Abstract
Given a submodular capacity space, we prove the uniform convergence in capacity and also the uniform convergence in the Choquet-mean of order p1 with a quantitative estimate, of the multivariate Bernstein polynomials associated to a random function. Applications to quantitative estimates concerning the uniform convergence in capacity in the univariate case are given.
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