Some modifications of the Dudley metric

Upper and lower bounds are obtained for the modified Dudley metric in terms of the Levy-Prokhorov metric.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 61, pp. 17–24, 1976.In conclusion, we want to thank V. M. Zolotarev for suggesting the problem and for his constant interest in this work.