2016/06/06 by Shaoxiong Hou, Hou, Shaoxiong, Deping Ye +1
Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities #Probability (math.PR) #math.MG #math.PR
paper · pdf · doi:10.48550/arxiv.1606.02155
arxiv created 2016/06/06 · openalex publication_date 2016/06/06 · arxiv updated 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the Orlicz addition of measures is proposed and an interpretation of the f-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional Orlicz-Brunn-Minkowski inequality, are established. We also investigate an optimization problem for the f-divergence and establish functional affine isoperimetric inequalities for the dual functional Orlicz affine and geominimal surface areas of measures.