---
tag: 63Z1Q4FS23
kind: concept
name: Finite measure
msc: [28A12]
specializes: [PR11BZQQPG]
sources:
  - url: https://en.wikipedia.org/wiki/Finite_measure
same_as:
  wikidata: Q3307145
  wikipedia: Finite measure
---

## Summary

A finite measure is a measure that gives the whole space a finite value.
Every measurable set then has finite measure.
Probability measures are the finite measures of total mass $1$, and every nonzero finite measure is a multiple of a probability measure.

## Explanations

### L1 human

A finite measure is a way of measuring in which the total amount is finite.
Length on the interval $[0, 1]$ is a finite measure, with total $1$.
Length on the whole real line is not, since the line is infinitely long.
Dividing a nonzero finite measure by its total gives a probability measure.