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 extension theorem | Statement: [measure theory, usesConcept, Carathéodory extension theorem]

Target entity: Carathéodory extension theorem
Context triple: [measure theory, usesConcept, Carathéodory extension theorem]

• A. Carathéodory’s extension theorem chosen
  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.
• B. Kolmogorov extension theorem
  The Kolmogorov extension theorem is a fundamental result in probability theory that guarantees the existence of a stochastic process with given consistent finite-dimensional distributions.
• C. 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.
• 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. Kolmogorov axioms
  The Kolmogorov axioms are the standard mathematical foundation of probability theory, formalizing probabilities as measures on a sigma-algebra that satisfy non-negativity, normalization, and countable additivity.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.