The Lévy radius of a set of probability measures satisfying basic moment conditions involving \(\{t,t^ 2\}\)
Let \(M(\epsilon_ 1,\epsilon_ 2)\) be the set of probability measures \(\mu\) satisfying \(| \int t^ jd\mu -s^ j_ 0| \leq \epsilon_ j\) for \(j=1,2\) with a real number \(s_ 0\). The author calculates the precise upper bound for the Lévy distance \(d_ L(\mu,\delta)\) between measures \(\mu\) in \(M(\epsilon_ 1,\epsilon_ 2)\) and the Dirac measure \(\delta\) concentrated at the point \(s_ 0\). The problem was motivated by \textit{P. P. Korovkin}'s theorem [Linear Operators and approximation theory. (1959; Zbl 0094.102), p. 6].
scientific article; zbMATH DE number 4020092
scientific article