Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:cardinality |
continuum (in ℝ)
|
| gptkbp:closed |
countable intersections
countable unions relative complements |
| gptkbp:contains |
all closed sets
all open sets |
| gptkbp:definedIn |
topological spaces
|
| gptkbp:defines |
the smallest σ-algebra containing all open sets in a topological space
|
| gptkbp:example |
gptkb:Cantor_set
countable sets in ℝ intervals in ℝ |
| gptkbp:field |
gptkb:topology
measure theory |
| gptkbp:hasHierarchy |
gptkb:Borel_hierarchy
|
| gptkbp:hasSubgroup |
measurable sets
|
| https://www.w3.org/2000/01/rdf-schema#label |
Borel sets
|
| gptkbp:importantFor |
gptkb:Borel_measure
Lebesgue measure |
| gptkbp:namedAfter |
gptkb:Émile_Borel
|
| gptkbp:notAll |
measurable sets are Borel sets
|
| gptkbp:notation |
𝔅 or 𝔅(X)
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:descriptive_set_theory real analysis |
| gptkbp:bfsParent |
gptkb:set-theoretic_topology
gptkb:descriptive_set_theory |
| gptkbp:bfsLayer |
6
|