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: [Banach–Tarski paradox, relatedTo, Vitali set]

Target entity: Vitali set
Context triple: [Banach–Tarski paradox, relatedTo, Vitali set]

• A. Vitali set chosen
  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.
• B. 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.
• C. Nikodym set
  A Nikodym set is a pathological subset of the plane in geometric measure theory that intersects almost every line in a very small (often measure-zero) way while still having full measure in a region, illustrating extreme irregular behavior of measurable sets.
• D. Sierpiński set
  The Sierpiński set is a subset of the real numbers with the property that it intersects every uncountable closed subset of the reals in only countably many points, illustrating extreme pathological behavior in set theory and real analysis.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.