▾ Set of symbols
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▾ Zermelo-Fraenkel set theory
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▾ Hyperpower set
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▾ Measure space
▾ Probability space
▾ Event
Event Shannon information
Formulation 0
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that
(i) $E \in \mathcal{F}$ is an D1716: Event in $P$
Let $\log_a$ be the D866: Standard real logarithm function in base $a \in (0, \infty)$ such that
(i) \begin{equation} \log_a 0 : = - \infty \end{equation}
The Shannon information of $E$ in $P$ in base $a$ is the D5237: Unsigned basic number \begin{equation} - \log_a \mathbb{P}(E) \in [0, \infty] \end{equation}
Child definitions
» D4392: Event Shannon bit information
» D4393: Event Shannon nat information