Definition of Borel Sigma-Algebra

Definition: The Borel sigma-algebra of a set S is the smallest sigma-algebra of S that contains all of the open balls in S. Any element of a Borel sigma-algebra is a Borel Set.

Example: The set B¹ is the Borel sigma-algebra of the real line, and thus contains every open interval.

Example: Consider a filled circle in the unit square. It can be constructed by a countable number of non-overlapping open rectangles (since a series of such rectangles can be defined that would cover every point in the circle but no point outside of it. Therefore it is in the smallest sigma-algebra of open subsets of the unit square.

Terms related to Borel Sigma-Algebra:

• Sigma-algebra
• Borel Set
• Measure

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Writing a Term Paper? Here are a few starting points for research on Borel Sigma-Algebra:

Journal Articles on Borel Sigma-Algebra:

• On a Theorem of Holický and Zelený Concerning Borel Maps Without sigma-Compact Fibers
• Moderation of sigma-finite Borel measures
• On sigma-discrete borel mappings via quasi-metrics