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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 35, Fasc. 2,
pages 247 - 266
 

EXTREMAL PROPERTIES OF ONE-DIMENSIONAL CAUCHY-TYPE MEASURES

T. Byczkowski
T. Żak

Abstract: 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 one-dimensional 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.

2000 AMS Mathematics Subject Classification: Primary: 60E05; Secondary: 60E07.

Keywords and phrases: Cauchy distribution, isoperimetry.

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