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Fall 2021

Niu, Yeli

This thesis includes 2 parts. Part 1 is: Discretization on High Dimensional Compact Do￾mains. Part 2 is: Polynomial Approximation on High Dimensional Spheres. A special example for part 1 is the result on the unit sphere of high-dimensional Euclidean spaces. In chapter 2, we obtained general

results about discretization of integration on compact met￾ric domains. Related results on spheres, closed balls and simplexed could be as special exam￾ples of our results. The first main result is about regular partitions on compact path-connected metric space equipped with non-atomic Borel probability

projects in these two directions and the progress I’ve made.