Definition:Borel Sigma-Algebra/Borel Set

Definition

Let $\struct {S, \tau}$ be a topological space.

Let $\map \BB {S, \tau}$ be the Borel $\sigma$-algebra of $\struct {S, \tau}$.

The elements of $\map \BB {S, \tau}$ are called the Borel (measurable) sets of $\struct {S, \tau}$.

Also see

• Results about Borel sets can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Borel set
• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $3.6$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Borel set
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Borel set