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: Lebesgue density theorem | Statement: [Steinhaus theorem, relatedTo, Lebesgue density theorem]

Target entity: Lebesgue density theorem
Context triple: [Steinhaus theorem, relatedTo, Lebesgue density theorem]

• A. Lebesgue differentiation theorem chosen
  The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
• B. 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.
• C. Borel–Lebesgue theorem
  The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
• D. Carathéodory measurability criterion
  The Carathéodory measurability criterion is a fundamental condition in measure theory that characterizes measurable sets via an outer measure by requiring additivity over intersections and complements.
• E. Nikodym convergence theorem
  The Nikodym convergence theorem is a fundamental result in measure theory that generalizes the Lebesgue dominated convergence theorem by characterizing when convergence of integrals holds under weaker conditions on the dominating measures.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.