AbstractIn this paper, the concept of the classical ƒ-divergence for a pair of measures is extended to the mixed ƒ-divergence formultiple pairs ofmeasures. The mixed ƒ-divergence provides a way to measure the diòerence between multiple pairs of (probability) measures. Properties for the mixed ƒ-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov–Fenchel type inequality and an isoperimetric inequality for the mixed ƒ-divergence are proved.
Isoperimetric inequality for radial probability measures on Euclidean spaces