Abstract In this paper, we introduce a generalized Hellinger distance between two monotone measures, including a derivative with respect to monotone measures. Then some properties of this distance are studied. We also obtain a lower bound for the generalized Hellinger distance. Finally, an error bound for the generalized Hellinger distance on conjugates is studied.

中文翻译：

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Choquet 积分的广义海灵格距离

摘要 在本文中，我们介绍了两个单调测度之间的广义 Hellinger 距离，包括关于单调测度的导数。然后研究了这个距离的一些性质。我们还获得了广义海灵格距离的下限。最后，研究了共轭上广义海灵格距离的误差界限。