Journal of Theoretical Probability

, Volume 9, Issue 2, pp 533–540 | Cite as

Zeros of the densities of infinitely divisible measures on R n

  • Tomasz Byczkowski
  • Balram S. Rajput
  • Tomasz Żak


Let μ be an infinitely divisible probability measure onR n without Gaussian component and let ν be its Lévy measure. Suppose that μ is absolutely continuous with respect to the Lebesgue measure λ. We investigate the structure of the set ℝ n of admissible translates of μ. This yields a unified presentation of previously known results. We also show that ifλ(S)>0 then μ is equivalent to λ, under the assumption that supp μ=R n , whereS is the closure of the semigroup generated by the support of ν.

Key Words

Infinitely divisible measures Poisson measures equivalence with Lebesgue measure 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Tomasz Byczkowski
    • 1
  • Balram S. Rajput
    • 2
  • Tomasz Żak
    • 1
  1. 1.Institute of MathematicsWrocław Technical UniversityWrocław
  2. 2.Departments of MathematicsThe University of TennesseeKnoxville

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