Vitali set
E956272
UNEXPLORED
A Vitali set is a classic example in real analysis of a subset of the real numbers that is not Lebesgue measurable, constructed using the axiom of choice.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Vitali set canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T11961317 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Vitali set Context triple: [Lebesgue measure, hasNonMeasurableSets, Vitali set]
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A.
Cantor set
The Cantor set is a classic fractal subset of the real line formed by repeatedly removing the open middle third of intervals, notable for being uncountable, perfect, nowhere dense, and having zero Lebesgue measure.
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B.
Vitali covering lemma
The Vitali covering lemma is a fundamental result in measure theory that provides conditions under which a collection of sets can be reduced to a disjoint subcollection that still covers almost all of the original set, and it underpins many key theorems in real analysis and differentiation.
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C.
Borel set
A Borel set is any set that can be formed from open (or equivalently closed) sets of a topological space through countable unions, intersections, and complements, forming the smallest σ-algebra containing all open sets.
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D.
Lusin–Souslin theorem
The Lusin–Souslin theorem is a fundamental result in descriptive set theory stating that the continuous injective image of a Borel set in a Polish space is again a Borel set.
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E.
Lebesgue measurable set
A Lebesgue measurable set is a subset of Euclidean space for which a consistent, translation-invariant notion of "size" (Lebesgue measure) can be assigned, forming the foundation of modern measure theory and integration.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Vitali set Target entity description: A Vitali set is a classic example in real analysis of a subset of the real numbers that is not Lebesgue measurable, constructed using the axiom of choice.
-
A.
Cantor set
The Cantor set is a classic fractal subset of the real line formed by repeatedly removing the open middle third of intervals, notable for being uncountable, perfect, nowhere dense, and having zero Lebesgue measure.
-
B.
Vitali covering lemma
The Vitali covering lemma is a fundamental result in measure theory that provides conditions under which a collection of sets can be reduced to a disjoint subcollection that still covers almost all of the original set, and it underpins many key theorems in real analysis and differentiation.
-
C.
Borel set
A Borel set is any set that can be formed from open (or equivalently closed) sets of a topological space through countable unions, intersections, and complements, forming the smallest σ-algebra containing all open sets.
-
D.
Lusin–Souslin theorem
The Lusin–Souslin theorem is a fundamental result in descriptive set theory stating that the continuous injective image of a Borel set in a Polish space is again a Borel set.
-
E.
Lebesgue measurable set
A Lebesgue measurable set is a subset of Euclidean space for which a consistent, translation-invariant notion of "size" (Lebesgue measure) can be assigned, forming the foundation of modern measure theory and integration.
- F. None of above. chosen
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.