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POWER INEQUALITY ON THE SIMPLEX

  • Baek, In-Soo (Department of Mathematics Busan University of Foreign Studies)
  • Published : 2012.05.15

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

References

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