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: Radon–Nikodym theorem | Statement: [Otton Nikodym, hasNotableTheorem, Radon–Nikodym theorem]

Target entity: Radon–Nikodym theorem
Context triple: [Otton Nikodym, hasNotableTheorem, Radon–Nikodym theorem]

• A. Radon–Nikodym derivative chosen
  The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
• B. 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.
• C. Lebesgue decomposition theorem
  The Lebesgue decomposition theorem is a fundamental result in measure theory that states any σ-finite measure can be uniquely decomposed into a part that is absolutely continuous with respect to another measure and a part that is singular to it.
• D. 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.
• E. Hahn decomposition theorem
  The Hahn decomposition theorem is a fundamental result in measure theory that states any signed measure space can be partitioned into a positive set and a negative set on which the measure is respectively nonnegative and nonpositive.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasNotableTheorem
Context triple: [Otton Nikodym, hasNotableTheorem, Radon–Nikodym theorem]

• A. hasTheorem
  Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
• B. hasTheoremNamedAfter chosen
  Indicates that a theorem is named in honor of or after a particular person or entity.
• C. hasNotableMathematician
  Indicates that an entity is associated with or linked to a mathematician who is considered notable or distinguished.
• D. hasTheory
  Indicates that an entity possesses, is associated with, or is characterized by a particular theory.
• E. notableTheorist
  Indicates that the subject is recognized as a significant or influential theorist in relation to the object or specified field.
• F. None of above.