---
tag: 0KTGJW1ZTH
kind: concept
name: Jordan measure
aliases: [jordan-content, peano-jordan-measure]
msc: [28A75]
uses: [0XPR1E85W0, 0WAR4F23B4]
sources:
  - url: https://en.wikipedia.org/wiki/Peano%E2%80%93Jordan_measure
    locator: Extension to more complicated sets
same_as:
  wikidata: Q1703597
  wikipedia: Peano–Jordan measure
---

## Summary

The Jordan measure, or Jordan content, extends the volume of boxes in [[R^n|0XPR1E85W0]] to some bounded sets. Finite unions of boxes approximate these sets well from inside and from outside.
A bounded set has Jordan measure exactly when its indicator function is Riemann integrable, and then the measure is the integral of that function.