Literature cited
V. M. Zolotarev, “The Mellin-Stieltjes transform in probability theory,”Teor. Veroyatn. i Prim.,2, No. 4, 444–469 (1957).
A. I. Plotkin, “On isometric operators on the spacesL p,”Dokl. Akad. Nauk SSSR,193, No. 3, 537–539 (1970).
A. I. Plotkin, “Extension ofL p-isometries,”Zap. Nauch. Sem. Len. Otd. Mat. Inst,22, 103–129 (1971).
W. Rudin, “L p-isometries and equimeasurability,”Indiana Univ. Math. J.,25, No. 3, 215–228 (1976).
W. Linde, “Moments and measures on Banach spaces,”Math. Ann.,258, 277–287 (1982).
A. L. Koldobskii, “On isometric operators in vector-valuedL p-spaces,”Zap. Nauch. Sem. Len. Otd. Mat. Inst.,107, 198–203 (1982).
E. A. Gorin and A. L. Koldobskii, “On potentials of measures in Banach spaces,”Sib. Mat. Zh.,28, No. 1, 65–80 (1987).
M. Sh. Braverman, “Characteristic properties of normal and stable distributions,”Teor. Veroyatn. i Prim.,30, No. 3, 440–448 (1985).
M. Sh. Braverman, “On a method of characterizing probability distributions,”Teor. Veroyatn. i Prim.,32, No. 3, 582–586 (1987).
N. I. Akhiezer,The Classical Moment Problem and some Related Questions in Analysis, Oliver & Boyd, Edinburgh (1965).
I. J. Schoenberg, “Metric spaces and positive definite functions,”Trans. Amer. Math. Soc.,44, No. 3, 552–563 (1938).
N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan,Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow (1985).
A. V. Bukhvalov, A. I. Veksler, and V. A. Geiler, “Normed Lattices,”Itogi Nauki i Tekhniki, Mat. Analiz,18, 125–184 (1980).
S. J. Bernau, “A note onL p-spaces,”Math. Ann.,200, No. 4, 281–286 (1973).
Additional information
Translated from:Problemy Ustoichivosti Stokhasticheskikh Modelei, Trudy Seminara, 1989, pp. 47–55.
Rights and permissions
About this article
Cite this article
Zinger, A.A., Kakosyan, A.V. & Klebanov, L.B. A characterization of distributions by mean values of statistics and certain probabilistic metrics. J Math Sci 59, 914–920 (1992). https://doi.org/10.1007/BF01099119
Issue Date:
DOI: https://doi.org/10.1007/BF01099119