Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
sigma-algebra |
| gptkbp:contains |
gptkb:Borel_sets
open sets closed sets complements of open sets countable intersections of open sets countable unions of open sets |
| gptkbp:definedIn |
gptkb:topology
|
| gptkbp:generation |
open sets
|
| gptkbp:hasSubgroup |
power set
|
| https://www.w3.org/2000/01/rdf-schema#label |
Borel sigma-algebra
|
| gptkbp:importantFor |
random variables
measurable functions definition of Borel measure definition of Lebesgue measure |
| gptkbp:isCountablyGenerated |
true
|
| gptkbp:isSigmaAlgebra |
true
|
| gptkbp:minimalSigmaAlgebraContaining |
open sets
closed sets |
| gptkbp:namedAfter |
gptkb:Émile_Borel
|
| gptkbp:notation |
𝔅
|
| gptkbp:onRealLine |
Borel sets of ℝ
|
| gptkbp:usedIn |
gptkb:probability_theory
measure theory real analysis |
| gptkbp:bfsParent |
gptkb:Borel_measure
|
| gptkbp:bfsLayer |
7
|