Contributions to Probability. A Collection of Papers by J. Gani, V. K. Rohatgi

By J. Gani, V. K. Rohatgi

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Nachr. 8 2 301-304, (1978). (In Russian) I. A. Ibragimov, On determining an infinitely divisible distribution function by its values on a half-line. Theory Prob. Applications 22 3 8 4 - 3 9 0 , (1977). V. M. Kruglov, Characterization of a certain class of infinitely divisible distributions in Hilbert space. Mat. Zametki 16 7 7 7 - 7 8 2 , (1974). (In Russian) H . - J . R o s s b e r g , B. J e s i a k , G . S i e g e l 48 [33] [34] Y u . V. Linnik and I. V. " Amer. Math. S o c , Providence, R. , 1977.

2 4 6 9 2 709, (1979). -J. Rossberg, Eigenschaften der charakteristischen Funktionen von einseitig beschrankten Verteilungsfunktionen und ihre Anwendung auf ein Charakterisierungsproblem der mathematischen Statistik. Math. Nachr. 3 7 3 7 - 5 7 , (1968). -J. Rossberg, A n extension of the Phragmen-Lindelof theory, which is relevant in characterization theory, in "A Modern Course on Statistical Distributions in Scientific Work" (G. D . Patil, S. Kotz, and J. K. ), Vol. 3. Dortrecht, Boston, 1975.

G exists in S't, then cP(Jg) ~ cP(J)cP(§). 2. We shall say: (1) a sequence ]" E S't, n = 1,2, ... , converges in norm cP, briefly cP-converges to J E S't ¢> cp(fn - f) ~ e in m; (2) a sequence ]" E 3 Un E S't, deC n = 1,2, ... , is cP-fundamental ¢> cp(]" - Jm) ~ o mdecreasing with Un! n - deC e ¢> such that 2' Vn = 1,2, In+k) ~ Un' Vk = 1,2, , . 1. If]" E S't, n = 1,2, 3 o-lim I(],,) Em. 2. If two sequences]" and gn E S't, n = 1,2, ... , Jlau-limfn = Jlau-limgn = J and moreover the two sequences are also cP-fundamental, then we have o-lim I(],,) = o-lim I(gn) E m.

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