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: Borel sigma-algebra | Statement: [Émile Borel, notableWork, Borel sigma-algebra]

Target entity: Borel sigma-algebra
Context triple: [Émile Borel, notableWork, Borel sigma-algebra]

• A. Borel set chosen
  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.
• B. Carathéodory’s extension theorem
  Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
• C. Baire space
  Baire space is a fundamental topological space—typically the set of all infinite sequences of natural numbers with the product topology—that serves as a central object in descriptive set theory and general topology.
• D. Lebesgue measure
  Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.