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2 results

  • Mixed ƒ-divergence for Multiple Pairs of Measures

  • Elisabeth Werner, Deping Ye
  • Journal:
    Canadian Mathematical Bulletin / Volume 60 / Issue 3 / 01 September 2017
    Published online by Cambridge University Press:
    20 November 2018, pp. 641-654
    Print publication:
    01 September 2017
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  • In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence formultiple pairs ofmeasures. The mixed $f$-divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed $f$-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov–Fenchel type inequality and an isoperimetric inequality for the mixed $f$-divergence are proved.

  • NEW RESULTS FOR T(k)-FAMILIES IN THE PLANE

  • Part of
  • Andreas F. Holmsen
  • Journal:
    Mathematika / Volume 56 / Issue 1 / January 2010
    Published online by Cambridge University Press:
    10 December 2009, pp. 86-92
    Print publication:
    January 2010

  • A line that intersects every member of a finite family F of convex sets in the plane is called a common transversal to F. In this paper we study some basic properties of T(k)-families: finite families of convex sets in the plane in which every subfamily of size at most k admits a common transversal. It is known that a T(k)-family admits a partial transversal of size α∣F∣ for some constant α(k) which is independent of F. Here it will be shown that (2/(k(k−1)))1/(k−2)≤α(k)≤((k−2)/(k−1)), which are the best bounds to date.