# Axiom:Axioms of Uncertainty/Axiom 6

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## Axiom

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:

- $H_n$ is a continuous function of its arguments.

## Sources

- 1988: Dominic Welsh:
*Codes and Cryptography*... (previous) ... (next): $\S 1$: Entropy = uncertainty = information: $1.1$ Uncertainty