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• Borel set
  ...ted by the open sets of a [[topological space]]. Thus, every open set is a Borel set, as are countable unions of open sets (i.e., unions of countably many open ...l space|topology]] of <math>X</math>). Then <math>A \subset X </math> is a Borel set of <math>X</math> if <math>A \in \sigma(O) </math>, where <math>\sigma(O)</
  981 bytes (168 words) - 13:28, 26 July 2008
• Non-Borel set
  ...and at most countable unions and intersections. (For the definition see [[Borel set]].) Only sets of real numbers are considered in this article. Accordingly, ...sin]], is described below. In contrast, an example of a non-measurable non-Borel set can only be proved to exist, but it cannot be constructed (because the exis
  2 KB (252 words) - 11:44, 2 December 2010
• Borel set/Approval
  12 bytes (1 word) - 13:08, 25 September 2007
• Borel set/Definition
  123 bytes (19 words) - 18:52, 24 June 2008
• Borel set/Related Articles
  260 bytes (36 words) - 13:28, 26 July 2008
• Non-Borel set/Bibliography
  292 bytes (32 words) - 03:39, 1 July 2009
• Non-Borel set/Definition
  A constructive example of a set of real numbers that is not a [[Borel set]].
  113 bytes (18 words) - 01:24, 19 June 2009
• Non-Borel set/Advanced
  ...l numbers ''x'' such that <math> a_0=3 </math> is an interval, therefore a Borel set. ...on "<math> a_1=3 </math>" leads to a countable union of intervals; still a Borel set.
  2 KB (402 words) - 20:47, 30 June 2009
• Non-Borel set/Related Articles
  {{r|Borel set}} -->
  217 bytes (31 words) - 10:31, 21 June 2009

Page text matches

• Non-Borel set
  ...and at most countable unions and intersections. (For the definition see [[Borel set]].) Only sets of real numbers are considered in this article. Accordingly, ...sin]], is described below. In contrast, an example of a non-measurable non-Borel set can only be proved to exist, but it cannot be constructed (because the exis
  2 KB (252 words) - 11:44, 2 December 2010
• Non-Borel set/Advanced
  ...l numbers ''x'' such that <math> a_0=3 </math> is an interval, therefore a Borel set. ...on "<math> a_1=3 </math>" leads to a countable union of intervals; still a Borel set.
  2 KB (402 words) - 20:47, 30 June 2009
• Non-Borel set/Definition
  A constructive example of a set of real numbers that is not a [[Borel set]].
  113 bytes (18 words) - 01:24, 19 June 2009
• Borel set
  ...ted by the open sets of a [[topological space]]. Thus, every open set is a Borel set, as are countable unions of open sets (i.e., unions of countably many open ...l space|topology]] of <math>X</math>). Then <math>A \subset X </math> is a Borel set of <math>X</math> if <math>A \in \sigma(O) </math>, where <math>\sigma(O)</
  981 bytes (168 words) - 13:28, 26 July 2008
• Sigma algebra
  * The set of all [[Borel set|Borel subsets]] of the [[real number|real line]] is a sigma-algebra. [[Borel set]]
  2 KB (314 words) - 16:35, 27 November 2008
• Non-Borel set/Related Articles
  {{r|Borel set}} -->
  217 bytes (31 words) - 10:31, 21 June 2009
• Measure theory/Related Articles
  {{r|Borel set}}
  771 bytes (95 words) - 18:24, 11 January 2010
• Random variable
  ...> where <math>\mathcal{B}(\mathbb{R})</math> is the [[sigma algebra]] of [[Borel set|Borel subsets]] of <math>\mathbb{R}</math> and ''P'' is a probability measu
  2 KB (383 words) - 17:06, 17 October 2007
• Almost sure convergence
  ...where <math>\mathcal{B}(\mathbb{C}^n)</math> is the [[sigma algebra]] of [[Borel set|Borel sets]] of <math>\mathbb{C}^n</math>. A formal definition of almost su
  2 KB (393 words) - 06:53, 14 July 2008
• Sigma algebra/Related Articles
  {{r|Borel set}}
  812 bytes (100 words) - 20:22, 11 January 2010
• Space (mathematics)
  ...le spaces (called also standard Borel spaces) are especially useful. Every Borel set (in particular, every closed set and every open set) in a Euclidean space (
  28 KB (4,311 words) - 08:36, 14 October 2010
• Statistics theory/Advanced
  ...'' which is [[measurable function|measurable]] (here with respect to the [[Borel set]]s of <math>\scriptstyle \mathbb{R}^N</math>). Two examples of commonly use
  9 KB (1,291 words) - 04:36, 27 June 2009
• Statistics theory
  ...'' which is [[measurable function|measurable]] (here with respect to the [[Borel set]]s of <math>\scriptstyle \mathbb{R}^N</math>). Two examples of commonly use
  15 KB (2,373 words) - 12:26, 20 February 2021