Inventiones mathematicae

, Volume 30, Issue 2, pp 207–216 | Cite as

The Brunn-Minkowski inequality in Gauss space

  • Christer Borell


Gauss Space 
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  1. 1.
    Badrikian, A.: Séminaire sur les fonctions aléatories linéaires et les mesures cylindriques. Lecture Notes in Mathematics139. Berlin-Heidelberg-New York: Springer 1970Google Scholar
  2. 2.
    Badrikian, A., Chevet, S.: Mesures, cylindriques, espaces de Wiener et aléatoires gaussiennes. Lecture Notes in Mathematics379. Berlin-Heidelberg-New York: Springer 1974Google Scholar
  3. 3.
    Blumenthal, R. M., Getoor, R. K.: Markov processes and potential theory. New York: Academic Press 1968Google Scholar
  4. 4.
    Borell, C.: Convex measures on locally convex spaces. Ark. Mat.,12, 239–252 (1974)Google Scholar
  5. 5.
    Borell, C.: Convex measures on product spaces and some applications to stochastic processes. Institut Mittag-Leffler, No. 3 (1974)Google Scholar
  6. 6.
    Borell, C.: Random linear functionals and subspaces of probability one. Institut Mittag-Leffler, No. 9 (1974)Google Scholar
  7. 7.
    Itô, K., McKean, H. P., Jr.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965Google Scholar
  8. 8.
    Fernique, X.: Intégrabilité des vecteurs gaussiens, C. R. Acad. Sci. Paris, Ser. A,270, 1698–1699 (1970)Google Scholar
  9. 9.
    Marcus, M.B., Shepp, L.A.: Sample behavior of Gaussian processes, Proc. of the Sixth Berkeley Symposium on Math. Stat. and Probability.2, 423–441 Berkeley 1972Google Scholar
  10. 10.
    Martineau, A.: Sur le théorème du graphe fermé. C. R. Acad. Sci. Paris, Ser. A,263, 870–871 (1966)Google Scholar
  11. 11.
    McKean, H.P.: Geometry of differential space. Ann. of Prob., Vol.1, 197–276 (1973)Google Scholar
  12. 12.
    Landau, H.J., Shepp, L.A.: On the supremum of a Gaussian process. Sankhyā, Ser. A.32, 369–378 (1971)Google Scholar
  13. 13.
    LaPage, R.: Subgroups of paths and reproducting kernels. Ann. of Prob.1, 354–347 (1973)Google Scholar
  14. 14.
    Poincaré, H.: Calcul des probabilités. Paris: Gauthier-Villars 1912Google Scholar
  15. 15.
    Schmidt, E.: Die Brunn-Minkowskische Ungleichung und ihr Spiegelbild sowie die isoperimetrische Eigenschaft der Kugel in der euklidischen und nichteuklidischen Geometrie. I. Math. Nach.I, 81–157 (1948)Google Scholar
  16. 16.
    Schwartz, L.: Sur le théorème du graphe fermé. C.R. Acad. Sci. Paris, Ser. A,263, 602–605 (1966)Google Scholar
  17. 17.
    Spitzer, F.: Electrostatic capacity, heat flow, and Brownian motion, Z. Wanrscheinlichkeitstheorie Verw. Geb.,3, 110–121 (1964)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Christer Borell
    • 1
  1. 1.Department of MathematicsUppsalaSweden

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