structural:expansion, stylistic:style_transfer
Discussion

It was shown that any function H {\displaystyle \mathrm {H} } satisfying the above properties must be a constant multiple of Shannon entropy, with a non-negative constant. Compared to the previously mentioned characterizations of entropy, this characterization focuses on the properties of entropy as a function of random variables (subadditivity and additivity), rather than the properties of entropy as a function of the probability vector p 1, …, p n {\displaystyle p_{1},\ldots,p_{n}}.

It is worth noting that if we drop the "small for small probabilities" property, then H {\displaystyle \mathrm {H} } must be a non-negative linear combination of the Shannon entropy and the Hartley entropy.