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
Filtered probability space
Random time
Stopping time
Negative binomial random number
Geometric random positive integer
Definition D4000
Standard exponential random positive real number
Formulation 0
Let $G_n \in \text{Geometric}(\theta_n)$ be a D4001: Geometric random positive integer for each $n \in 1, 2, 3, \ldots$ such that
(i) \begin{equation} \forall \, n \in \{ 1, 2, 3, \ldots \} : \theta_n = \frac{1}{n} \end{equation}
A D5722: Random positive real number $X \in \text{Random}(0, \infty)$ is a standard exponential random positive real number if and only if \begin{equation} X \overset{d}{=} \lim_{n \to \infty} \frac{G_n}{n} \end{equation}
Children
D214: Exponential random positive real number