A proof of Mikusiński's theorem on bounded moments with Bernstein polynomials (Q1107059)

The theorem of bounded moments is a very useful mathematical tool and it attracted the interest of many mathematicians. This theorem has many different forms and it has been proved in many different ways. One of the simplest proof was given by \textit{J. Mikusiński} and \textit{C. Ryll- Nardzewski} [Stud. Math. 13, 51-55 (1953; Zbl 0050.106)]. The proof in this paper is a new one. It is based on the generalized Bernstein polynomials and the growth of the coefficients of these polynomials.