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
▼ Independent event collection
▼ Independent collection of event collections
▼ Independent collection of sigma-algebras
▼ Independent random collection
Definition D3358
I.I.D. random collection
Formulation 0
A D1721: Random collection $X : J \to \text{Random}(\Omega \to \Xi)$ is independent and identically distributed if and only if
(1) $X$ is an D2713: Independent random collection
(2) $X$ is an D3357: Identically distributed random collection
Children
▶ Strong white noise random real collection
Results
▶ R5424
▶ I.I.D. real central limit theorem
▶ I.I.D. real weak law of large numbers under finite second absolute moments
▶ I.I.D. weak law of large numbers for random real numbers
▶ Standard I.I.D. real central limit theorem