##  [Borel Sigma-Algebra](/borel-sigma-algebra) 

  ##  [Borel Sigma-Algebra](https://natural.quantumdictionary.io/borel-sigma-algebra-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The smallest sigma-algebra on a topological space generated by its open sets (equivalently by its closed sets or by a base of the topology), whose elements are called Borel sets and which provides the minimal measurable structure compatible with the topology.

 

 

 

 

 





 

 



 ##  [Borel Sigma-Algebra](https://puremath.quantumdictionary.io/borel-sigma-algebra-1) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The sigma-algebra generated by the open sets of a topological space; its members are called Borel sets and are all sets that can be formed from open sets by countable unions, countable intersections and complements.