论文标题
在Choquet集成理论框架中，随机多项式对随机函数的近似
Approximation of Random Functions by Random Polynomials in the Framework of Choquet's Theory of Integration
论文作者
论文摘要
给定一个下能力空间，我们证明了容量的均匀收敛，也证明了与随机函数相关的多变量伯恩斯坦多项式的定量估计值$ p \ ge1 $中的均匀收敛。给出了有关单变量案例中均匀融合均匀收敛的定量估计的应用。
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.
