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: Carathéodory construction of measures | Statement: [Carathéodory measurability criterion, basedOn, Carathéodory construction of measures]

Target entity: Carathéodory construction of measures
Context triple: [Carathéodory measurability criterion, basedOn, Carathéodory construction of measures]

• A. Carathéodory measurability criterion chosen
  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.
• 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. Hausdorff measure
  Hausdorff measure is a fundamental concept in geometric measure theory that generalizes the notion of length, area, and volume to sets with arbitrary fractal or irregular structure in metric spaces.
• D. Marczewski measure
  The Marczewski measure is a concept in measure theory that generalizes classical measures to study the size and structure of sets, particularly in relation to category and descriptive set theory.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.