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Construction junctions are diamonds. They show where multiple structures must coexist on the same carrier and satisfy compatibility conditions.

Canonical static concept record

Measurable function

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Summary

A function whose inverse images of measurable sets are measurable.

Record metadata

Canonical name: Measurable function
Concept ID: measurable_function
Content version: 2.3.0
Primary field: Mathematics
Fields: Mathematics
Primary domain: Measure
Domains: Measure
Alternate terminology: No alternate terminology is currently authored for this record.

Carrier(s)

measurable spaces $(X,\Sigma)$ and $(Y,\mathcal T)$

Data

function $f\colon X\to Y$

Axioms / constraints

$f^{-1}(B)\in\Sigma$ for every $B\in\mathcal T$

Notes

Both domain and codomain measurable structures are part of the specification; measurability is not a property of a bare function alone.

Concept sources

Wikipedia — Measurable function — Measurable function · expository · source ID wp-measurable-function
nLab — Measurable function — Measurable function · mathematical reference · source ID nlab-measurable-function
Tao — An Introduction to Measure Theory — An Introduction to Measure Theory · textbook · source ID tao-measure-theory

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

function + measurable domain/codomain(construction junction)Measurable function

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: j_measurable_function__out
Relation type: Combine compatible structures combine-compatible
Direction: source → target
Endpoint roles: source: Builds toward; target: Built from
Authored annotation: impose measurability

Authored explanation

Require inverse images of measurable codomain sets to be measurable in the domain.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Wikipedia — Measurable function — Measurable function · expository · source ID wp-measurable-function
Tao — An Introduction to Measure Theory — An Introduction to Measure Theory · textbook · source ID tao-measure-theory

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.