Axiom:Axioms of Uncertainty/Axiom 7

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Let $Z$ be a random variable.

Let $Z$ take the values $a_i$ with probability $p_i$, where $i \in \set {1, 2, \ldots, n}$.

Let $H_n: Z^n \to \R$ be a mapping which is to be defined as the uncertainty of $Z$.

${H_n}$ fulfils the following axiom:

$\map {H_{m n} } {\dfrac 1 {m n}, \dfrac 1 {m n}, \dotsc, \dfrac 1 {m n} } = \map {H_m} {\dfrac 1 m, \dfrac 1 m, \dotsc, \dfrac 1 m} + \map {H_n} {\dfrac 1 n, \dfrac 1 n, \dotsc, \dfrac 1 n}$