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A characterization of the Cauchy type. (English) Zbl 0341.60009

MSC:
60E05 Probability distributions: general theory
28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
28A20 Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence
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[1] William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. · Zbl 0077.12201
[2] F. B. Knight and P. A. Meyer, Une caract√©risation de la loi de Cauchy, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 34 (1976), no. 2, 129 – 134. · Zbl 0353.60020 · doi:10.1007/BF00535680 · doi.org
[3] E. J. G. Pitman and E. J. Williams, Cauchy-distributed functions of Cauchy variates, Ann. Math. Statist. 38 (1967), 916 – 918. · Zbl 0201.51104 · doi:10.1214/aoms/1177698885 · doi.org
[4] H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. · Zbl 0121.05501
[5] E. J. Williams, Cauchy-distributed functions and a characterization of the Cauchy distribution, Ann. Math. Statist. 40 (1969), 1083 – 1085. · Zbl 0184.22602 · doi:10.1214/aoms/1177697613 · doi.org
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