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A survey about zero-one laws for probability measures on linear spaces and locally compact groups

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Probability Measures on Groups VII

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References

  • Baker, C.R. (1973). Zero-one laws for Gaussian measures on Banach spaces. Trans. Amer. Math. Soc. 186, 291–308. MR 49 # 1569.

    Article  MathSciNet  MATH  Google Scholar 

  • Byczkowska, H., Byczkowski, T., (1981). A generalization of the zero-one law for Gaussian measures on metric Abelian groups. Bull. l'Acad. Polon. Sc., Sér. Math. 29, 187–191.

    MathSciNet  MATH  Google Scholar 

  • Byczkowski, T. (1977) a). Gaussian measures on Lp spaces, 0≤p<∞. Studia Math. 59, 249–261. MR 56 # 6777.

    MathSciNet  MATH  Google Scholar 

  • Byczkowski, T. (1977) b). Some results concerning Gaussian measures on metric spaces. Lect. Notes Math. 656, 1–16, Springer-Verlag. MR 80j: 60021.

    Google Scholar 

  • Byczkowski, T. (1978). Gaussian measures on metric Abelian groups. In Probability measures on groups. Proc. Oberwolfach. Lect. Notes Math. 706, 41–53. Springer. MR 80k: 60013.

    Article  MathSciNet  Google Scholar 

  • Byczkowski, T. (1980). Zero-one laws for Gaussian measures on metric Abelian groups. Studia Math. 69,159–189.

    MathSciNet  MATH  Google Scholar 

  • Byczkowski, T., Hulanicki, A. (1983). Gaussian measure of normal subgroups. Annals of Probability (in print).

    Google Scholar 

  • Cambanis, S. Rajput, B. S. (1973). Some zero-one laws for Gaussian processes. Ann. Prob. 1, 304–312. MR 52 # 6851.

    Article  MathSciNet  MATH  Google Scholar 

  • Cameron, R.H., Graves, R.E. (1951). Additive functionals on a space of continuous functions. I. Trans. Amer. Math. Soc. 70, 160–176. MR 12 # 718.

    Article  MathSciNet  MATH  Google Scholar 

  • Chatterji, S.D., Mandrekar, V. (1978). Equivalence and singularity of Gaussian measures and applications. In: Probabilistic analysis and related topics, 169–195. Edited by A.T. Bharucha-Reid. Academic press, London.

    Google Scholar 

  • Chatterji, S.D., Ramaswamy, S. (1982). Mesures Gaussiannes et mesures produit. Lect. Notes Math. 920, 570–580. Springer.

    Article  MathSciNet  MATH  Google Scholar 

  • Dudley, R.M., Kanter, M. (1974). Zero-one laws for stable measures. Proc. Amer. Math. Soc. 45, 245–252. MR 51 # 6901.

    Article  MathSciNet  MATH  Google Scholar 

  • Fernique, X.M. (1974). Une démonstration simple du théorème de R.M. Dudley et M. Kanter sur les loi 0–1 pour les mesures stables. Séminaire de Prob. VII. Lect. Notes Math. 381, 78–79. Springer. MR 53 # 6664.

    Article  MathSciNet  Google Scholar 

  • Graham, C. C., McGehee, O. C. (1979). Essays in commutative harmonic analysis. Grundlehr. d. math. Wissensch. 238, Springer Verlag.

    Google Scholar 

  • Hazod, W. (1977). Stetige Faltungshalbgruppen und erzeugende Distributionen. Lect. Notes Math. 595. Springer.

    Google Scholar 

  • Heyer, H. (1977). Probability measures on locally compact groups. Ergebnisse d. Math. u. ihrer Grenzgebiete. Springer.

    Google Scholar 

  • Inglot, T. (1979). An elementary approach of the zero-one laws for Gaussian measures. Colloqu. Math. 40, 319–325. MR 80j: 60012.

    MathSciNet  MATH  Google Scholar 

  • Jain, N.C. (1971). A zero-one law for Gaussian processes. Proc. Amer. Math. Soc. 29, 585–587. MR 43 # 4099.

    Article  MathSciNet  MATH  Google Scholar 

  • Jamison, B. Orey, S. (1970). Subgroups of sequences and paths. Proc. Amer. Math. Soc. 24, MR 40 # 8121.

    Google Scholar 

  • Janssen, A. (1980). A general purity law for convolution semigroups with discrete Lévy measure. Semigroup Forum 20, 55–71.

    Article  MathSciNet  MATH  Google Scholar 

  • Janssen, A. (1982) a). Zero-one laws for infinitely divisible probability measures on groups. Z. Wahrscheinlichkeitstheorie verw. Geb. 60, 119–138.

    Article  MathSciNet  MATH  Google Scholar 

  • Janssen, A. (1982) b). Some zero-one laws for semistable and self-decomposable measures on locally convex spaces. In: Probability measures on groups. Proc. Oberwolfach. Lect. Notes Math. 928, 236–246. Springer.

    Article  MathSciNet  MATH  Google Scholar 

  • Kallianpur, G. (1970). Zero-one laws for Gaussian processes. Trans. Amer. Math. Soc. 149, 199–221. MR 42 # 1200.

    Article  MathSciNet  MATH  Google Scholar 

  • Krakowiak, W. (1978). Zero-one laws for stable and semi-stable measures on Banach spaces. Bull. d. l'acad. Polon., ser. sci. math. 27, 1045–1049. MR 80i: 60005.

    MathSciNet  MATH  Google Scholar 

  • Louie, D., Rajput, B. Tortrat, A. (1980). A zero-one dichotomy theorem for r-semistable laws on infinite dimensional linear spaces. Sankhyā, Ser. A. 42, 9–18.

    MathSciNet  MATH  Google Scholar 

  • Rajput, B. (1972). Gaussian measures on Lp spaces, 1≤p≤∞. J. Mult. Anal. 2, 382–403. MR 49 # 9896.

    Article  MathSciNet  MATH  Google Scholar 

  • Rajput, B., Louie, D., Tortrat, A, (1981). Une loi zéro-un pour une class de mesures sur les groupes. Ann. Inst. Henri Poincaré 17, 331–335.

    MATH  Google Scholar 

  • Rajput, B., Tortrat, A. (1980). Un théorème de probabilité zéro ou un dans un groupe mesurable ou topologique quelconque. C.R. Acad. Sc. Paris, t. 290, Sér. A., 251–254.

    MathSciNet  MATH  Google Scholar 

  • Shepp, L.A. (1966). Radon-Nikodym derivatives of Gaussian measures. Ann. Math. Statist. 37, 321–354. MR 32 # 8408.

    Article  MathSciNet  MATH  Google Scholar 

  • Siebert, E. (1982). Absolute continuity, singularity, and supports of Gauss semigroups on a Lie group. Mh. Math. 93, 239–253.

    Article  MathSciNet  MATH  Google Scholar 

  • Tortrat, A. (1980). Lois de zéro-un pour des probabilités semi-stables ou plus générales, dans un espace vectoriel ou un groupe (abélien ou non). Publication du C.N.R.S., Colloque de Saint-Flour.

    Google Scholar 

  • Tortrat, A. (1981). Loi stables dans un groupe. Ann. Inst. Henri Poincaré 17, 51–61. MR 82m: 60012.

    MathSciNet  MATH  Google Scholar 

  • Tortrat, A. (1982). Loi de zéro-un et lois semi-stables dans un group. In: Probability measures on groups. Proc. Oberwolfach. Lect. Notes Math. 928, 452–465.

    Article  MathSciNet  MATH  Google Scholar 

  • Varberg, D.E. (1967). Equivalent Gaussian measures with a particularly simple Radon-Nikodym derivative. Ann. Math. Statist. 38, 1027–1030. MR 35 # 4981.

    Article  MathSciNet  MATH  Google Scholar 

  • Zinn, J. (1974). Zero-one laws for non-Gaussian measures. Proc. Amer. Math. Soc. 44, 179–185. MR 49 # 9897.

    Article  MathSciNet  MATH  Google Scholar 

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Herbert Heyer

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Janssen, A. (1984). A survey about zero-one laws for probability measures on linear spaces and locally compact groups. In: Heyer, H. (eds) Probability Measures on Groups VII. Lecture Notes in Mathematics, vol 1064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073661

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  • DOI: https://doi.org/10.1007/BFb0073661

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