任意$f$的一个下界--关于全变差的散度
A Lower Bound on Arbitrary $f$--Divergences in Terms of the Total Variation
摘要：
量化两个概率测度相似性的一个重要工具是f-散度，它在统计学和信息论中有着广泛的应用。一个例子是全变差，它在f-发散中起着特殊的作用。证明了每一个f-散度都是由全变差的单调函数从下而上有界的。在适当的正则性条件下，该函数是单调的。注：主命题的证明相对容易，因此结果很可能是已知的。作者将非常感谢任何有关参考资料或相关工作的信息。
英文摘要：
An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among the f-divergences. It is shown that every f-divergence is bounded from below by a monotonous function of the total variation. Under appropriate regularity conditions, this function is shown to be monotonous. Remark: The proof of the main proposition is relatively easy, whence it is highly likely that the result is known. The author would be very grateful for any information regarding references or related work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
