Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Vitali set | Statement: [Lebesgue measure, hasNonMeasurableSets, Vitali set]

Target entity: Vitali set
Context triple: [Lebesgue measure, hasNonMeasurableSets, Vitali set]

• 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
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Vitali set
Triple: [Lebesgue measure, hasNonMeasurableSets, Vitali set]

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.

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

Target predicate: hasNonMeasurableSets
Context triple: [Lebesgue measure, hasNonMeasurableSets, Vitali set]

• A. hasLebesgueMeasure
  Indicates that a set is assigned a specific value by the Lebesgue measure, representing its "size" in the sense of measure theory.
• B. isUncountablePerfectNowhereDenseSubsetOfR
  Indicates that one set is a subset of the real numbers that is uncountable, perfect (closed with no isolated points), and nowhere dense (its closure has empty interior).
• C. measurability
  Indicates that a quantity, property, or outcome can be defined, quantified, or assessed using a consistent measurement framework.
• D. isNowhereDense
  Indicates that a set is so sparse in the space that the closure of the set has empty interior, meaning it contains no nontrivial open subset.
• E. isBaireCategory
  Indicates that a space (or set) satisfies the Baire category property, meaning countable intersections of dense open subsets remain dense in that space.
• F. None of above. chosen