Extremal properties of one-dimensional Cauchy- type measures

  1. Tomasz Byczkowski
  2. Tomasz Żak


In the paper we investigate some extremal properties of intervals for the one-dimensional Cauchy measure, related to isoperimetric inequalities. We also consider the analogous properties for the onedimensional sections of the multidimensional isotropic Cauchy measure. In particular, among intervals with the fixed measure we find the ones with the extremal measure of the boundary. It turns out that, contrary to the Gaussian case, the type of extremal set depends on the value of the measure.

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Probability and Mathematical Statistics

35, z. 2, 2015

Pages from 247 to 266

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