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arXiv 2003.143012020-03math.CA

Approximation of Random Functions by Random Polynomials in the Framework of Choquet's Theory of Integration

Sorin G. Gal, Constantin Niculescu

备注：: 18 pages

英文摘要：

Given a submodular capacity space, we prove the uniform convergence in capacity and also the uniform convergence in the Choquet-mean of order $p\ge1$ 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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