---
tag: 0WQXY32Q8D
kind: concept
name: Borel sigma-algebra
aliases: [borel-algebra, borel-set, borel-sets]
msc: [28A05]
sources:
  - url: https://en.wikipedia.org/wiki/Borel_set
    locator: lead section
same_as:
  wikidata: Q21086747
  wikipedia: Borel set
---

## Summary

The Borel σ-algebra of a topological space is the smallest σ-algebra that contains all open sets. Its elements are the Borel sets.
On the real line it is the usual family of events for real random variables. The node [[Borel sigma-algebra|0BVHZXWKCD]] gives the precise definition.