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：我们证明了Sharma-Mittal熵在所有$n$维概率分布构成的格上（该格按照向量间主序定义的偏序关系排序）是次可加且超模的函数。该结果统一并拓展了文献中针对Shannon熵、Tsallis熵和Rényi熵的类似结论。