---
tag: VQQM4Y550T
kind: concept
name: Null set
msc: [28A12, 28A05]
sources:
  - url: https://en.wikipedia.org/wiki/Null_set
same_as:
  wikidata: Q1201815
  wikipedia: Null set
---

## Summary

A null set in a measure space is a measurable set of measure zero.
Null sets are the sets that measure theory can ignore: changing a function on a null set does not change its integral.
For Lebesgue measure, every countable set is null, and so is the Cantor set.

## Explanations

### L1 human

A null set is a set that is too thin to have any size.
A single point on the line has length zero, and so does any countable list of points.
Even some uncountable sets, such as the Cantor set, have length zero.
In measure theory, what happens on a null set does not matter.