| Abstract: | The concept is introduced of a distribution function given by means of a sequence of finite-step functions that converges in the integral metric. (As shown in 1], the pointwise representation of a constructive distribution function at all points is not possible.) It is shown that there is a correspondence between constructive distributive functions and constructive characteristic functions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 60, pp. 59–64, 1976. Results announced December 20, 1973 and June 12, 1975.The author thanks N. A. Shanin for prolonged attention to the subject of this article and for critical remarks leading to the appearance of Secs. 2 and 3, as well as A. O. Slisenko, who pointed out isolated errors. |
