We prove that Sharma-Mittal entropy is a subadditive and supermodular function on the lattice of all $n$-dimensional probability distributions, ordered according to the partial order relation defined by majorization among vectors. Our result unifies and extends analogous results presented in the literature for the Shannon entropy, the Tsallis entropy, and the Rényi entropy.

翻译：摘要：我们证明了Sharma-Mittal熵在所有$n$维概率分布构成的格（该格上向量之间的偏序关系由主化定义）上是一个次可加且超模的函数。我们的结果统一并推广了文献中针对香农熵、Tsallis熵和Rényi熵所提出的类似结论。