Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Luzin's_theorem
|
| gptkbp:appliesTo |
measurable functions
finite measure spaces |
| gptkbp:field |
real analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lusin's theorem
|
| gptkbp:implies |
measurable functions are nearly continuous
|
| gptkbp:namedAfter |
gptkb:Nikolai_Luzin
|
| gptkbp:publishedIn |
1912
|
| gptkbp:relatedTo |
gptkb:Egorov's_theorem
approximation theory |
| gptkbp:state |
For every measurable function f on a finite measure set and every ε > 0, there exists a continuous function g such that the measure of the set where f ≠ g is less than ε.
|
| gptkbp:usedIn |
gptkb:Lebesgue_integration
measure theory |
| gptkbp:bfsParent |
gptkb:Luzin's_theorem
|
| gptkbp:bfsLayer |
7
|