ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Measurable space
Measure space
Probability space
Event
Event Shannon information
Definition D4393
Event Shannon nat 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 $\log$ be the D865: Standard natural real logarithm function such that
(i) \begin{equation} \log 0 : = - \infty \end{equation}
The Shannon nat information of $E$ in $P$ is the D5237: Unsigned basic number \begin{equation} - \log \mathbb{P}(E) \in [0, \infty] \end{equation}