Geodesic
On extension of $f$-divergence
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 3, pp. 468-489 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a lower semicontinuous convex function $f:\mathbf{R}\to\mathbf{R}\cup\{+\infty\}$, $\mathrm{dom}\,f\subseteq\mathbf{R}_+$, we give a definition and study properties of the $f$-divergence of finitely additive set functions $\mu$ and $\nu$ given on a measurable space $(\Omega,\mathscr{F})$. If $f$ is finite on $(0,+\infty)$ and $\mu$ and $\nu$ are probability measures, our definition is equivalent to the classical definition of the $f$-divergence introduced by Csiszár. As an application, we obtain a result on attaining the minimum by the $f$-divergence over a set $\mathscr{Z}$ of pairs of probability measures.
Mots-clés : $f$-divergence
Keywords: finitely additive set function. 
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A. A. Gushchin. On extension of $f$-divergence. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 3, pp. 468-489. http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a3/

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