An extremal property of the uniform distribution and some of its consequences. (English. Russian original) Zbl 0967.60012
Theory Probab. Appl. 44, No. 3, 583-588 (1999); translation from Teor. Veroyatn. Primen. 44, No. 3, 646-650 (1999).
Summary: An extremal property of monotone function mean value of random variables with uniformly bounded densities is established. As a consequence, optimal upper bounds are obtained for characteristic functions of such a type of random variables.
