measurable function

Function between measurable spaces

EntityQ516776

Subclass of: function

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is in direct analogy to the definition that a continuous function between topological spaces preserves the topological structure: the preimage of any open set is open. In real analysis, measurable functions are used in the definition of the Lebesgue integral. In probability theory, a measurable function on a probability space is known as a random variable.

Overview

All data

13 statements · 31% with external sources · numbers in brackets are citations

Defining formula: f^{-1}(E) = \{ x\in X |\; f(x) \in E \} \in \Sigma,\;\; \forall E \in \Tau

On other databases

11 identifiers linking measurable function across the web's reference databases

Data quality

statements

31%

externally sourced

Source last edited July 2, 2026. AIDB refreshes this page daily.

Suggest a fact or correction

Links

Use this data

curl https://aidb.si/api/v1/entities/Q516776

API docs, limits & keys

Cite this page

AIDB. (2026). measurable function (Q516776). Retrieved from https://aidb.si/e/measurable-function-Q516776