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Support and seminorm integrability theorems for r-semistable probability measures on LCTVS

  • Donald Louie
  • Balram S. Rajput
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 828)

Abstract

Let μ be an r-semistable K-regular probability measure of index α ε (0, 2] on a complete locally convex topological vector space E. It is shown that the topological support Sμ of μ is a translated convex cone if α ε (0, 1), and a translated truncated cone if α ε (1, 2]. Further, if α=1 and μ is symmetric, then it is shown that Sμ is a vector subspace of E. These results subsume all earlier known results regarding the support of stable measures. A result regarding the support of infinitely divisible probability measure on E is also obtained. A seminorm integrability theorem is obtained for K-regular r-semistable probability measures μ on E. The result of de Acosta (Ann. of Probability, 3(1975), 865 – 875) and Kanter (Trans. Seventh Prague Conf., (1974), 317 – 323) is included in this theorem as long as the measures are defined on LCTVS and seminorm is continuous.

Keywords

Hilbert Space Probability Measure Convex Cone Topological Vector Space Stable Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Donald Louie
    • 1
  • Balram S. Rajput
    • 2
    • 3
  1. 1.Department of MathematicsThe University of TennesseeKnoxvilleUSA
  2. 2.Department of MathematicsThe University of TennesseeKnoxvilleUSA
  3. 3.Indian Statistical InstituteNew DelhiIndia

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