Weierstrass Polynomial Approximation Theorem for $C[0,1]$ via Weak Law of Large Numbers


Krishna Athreya


Iowa State University
Department of Statistics
2438 Osborn Dr. Ames
Iowa 50011-4040
United States of America


Monday, 25 July 2016, 16:00 to 17:00



Karl Weierstrass showed that given a continuous function $f$ on $[0,1]$ and an epsilon positive, there is a polynomial $p$ such that it is uniformly epsilon close to $f$ on $[0,1]$. In this talk we give a proof  of this using coin tossing.  We then generalize this to the case of simplexes and hypercubes. We also discuss approximation by $C^{\infty}$ infinity functions using Gauss kernels.