Axiom:Axioms of Uncertainty

Axiom Schema
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 $H: Z^n \to \R$ be a mapping which is to be defined as the uncertainty of $Z$. Then $H$ fulfils the following conditions, which are to be known as the axioms of uncertainty: