random element

Generalization of the concept of random variable to more complicated spaces than the simple real line

EntityQ166211

Subclass of: variable
, function
Part of: probability theory

Overview

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In probability theory, random element is a generalization of the concept of random variable to more complicated spaces than the simple real line. The concept was introduced by Maurice Fréchet who commented:[the] development of probability theory and expansion of area of its applications have led to necessity to pass from schemes where (random) outcomes of experiments can be described by number or a finite set of numbers, to schemes where outcomes of experiments represent, for example, vectors, functions, processes, fields, series, transformations, and also sets or collections of sets.

Overview

All data

8 statements · 25% with external sources · numbers in brackets are citations

Defining formula: X:\Omega\to E
Definition domain: sample space in defining formula: \Omega
Image of function: measurable set in defining formula: E

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3 identifiers linking random element across the web's reference databases

Data quality

statements

25%

externally sourced

Source last edited October 6, 2026. AIDB refreshes this page daily.

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AIDB. (2026). random element (Q166211). Retrieved from https://aidb.si/e/random-element-Q166211