Carathéodory's extension theorem
GPTKB entity
Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
algebras of sets
pre-measures sigma-algebras |
| gptkbp:field |
measure theory
|
| https://www.w3.org/2000/01/rdf-schema#label |
Carathéodory's extension theorem
|
| gptkbp:namedAfter |
gptkb:Constantin_Carathéodory
|
| gptkbp:publicationYear |
1914
|
| gptkbp:publishedIn |
gptkb:Mathematische_Annalen
|
| gptkbp:state |
A pre-measure defined on an algebra of sets can be extended to a measure on the sigma-algebra generated by the algebra.
|
| gptkbp:usedFor |
constructing measures
defining Lebesgue measure |
| gptkbp:bfsParent |
gptkb:Measure_Theory
|
| gptkbp:bfsLayer |
5
|