Stability of characterization of a degenerate distribution
It is evident that if \(F=F^ 2\) and \(F\) is a distribution function, then \(F\) is degenerate. Now let the Lévy distance between the distribution functions \(F\) and \(F^ 2\) not exceed \(\varepsilon\). Then the distance between F and the class of all degenerate distributions does not exceed \(c\varepsilon\ln 1/\varepsilon\), where \(c\) is some absolute constant. The order of this estimate cannot be improved.
scientific article; zbMATH DE number 4034846