Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Lusin's_theorem
|
| gptkbp:appliesTo |
Lebesgue measure
measurable functions |
| gptkbp:field |
real analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Luzin's theorem
|
| gptkbp:importantFor |
shows measurable functions are nearly continuous
|
| gptkbp:namedAfter |
gptkb:Nikolai_Luzin
|
| gptkbp:publishedIn |
1912
|
| gptkbp:relatedTo |
gptkb:Egorov's_theorem
gptkb:Lebesgue's_differentiation_theorem |
| gptkbp:sentence |
For every measurable function f on a subset E of the real numbers and every ε > 0, there exists a closed set F ⊆ E such that the measure of E \\ F is less than ε and the restriction of f to F is continuous.
|
| gptkbp:bfsParent |
gptkb:Nikolai_Luzin
|
| gptkbp:bfsLayer |
6
|