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http://dx.doi.org/10.14403/jcms.2012.25.2.313

POWER INEQUALITY ON THE SIMPLEX  

Baek, In-Soo (Department of Mathematics Busan University of Foreign Studies)
Publication Information
Journal of the Chungcheong Mathematical Society / v.25, no.2, 2012 , pp. 313-318 More about this Journal
Abstract
The power inequality ${\prod}_{k=1}^{N}\;{x}_{k}^{x_{k}}\;{\geq}\;{\prod}_{k=1}^{N}\;{p}_{k}^{x_{k}}$ holds for the points $(x_1,{\ldots},x_N),(p_1,{\ldots},p_N)$ of the simplex. We show this using the analytic method combining Frostman's density theorem with the strong law of large numbers.
Keywords
simplex; strong law of large numbers; density theorem; Hausdorff dimension;
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