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
▼ Measurable map
▼ Random variable
▼ Uniform random variable
Definition D4624
Standard unsigned uniform random real number
Formulation 3
Let $X_1, X_2, X_3, \ldots \in \text{Bernoulli}(1/2)$ each be a D3999: Standard Bernoulli random boolean number such that
(i) $X_1, X_2, X_3, \ldots$ is an D2713: Independent random collection
A D3161: Random real number $U \in \text{Random}(0, 1)$ is a standard unsigned uniform random real number if and only if \begin{equation} U \overset{d}{=} \lim_{N \to \infty} \sum_{n = 1}^N \frac{X_n}{2^n} \end{equation}
Children
▶ D5901: Logistic random real number