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: Fubini's theorem for Lebesgue integrals | Statement: [Fubini's theorem, hasVersion, Fubini's theorem for Lebesgue integrals]

Target entity: Fubini's theorem for Lebesgue integrals
Context triple: [Fubini's theorem, hasVersion, Fubini's theorem for Lebesgue integrals]

• A. Fubini's theorem chosen
  Fubini's theorem is a fundamental result in measure theory that allows the evaluation of double integrals as iterated integrals under suitable integrability conditions.
• B. Lebesgue integration
  Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
• C. 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.
• D. Vitali convergence theorem
  The Vitali convergence theorem is a result in measure theory that gives conditions under which pointwise convergence of a sequence of integrable functions implies convergence of their integrals, strengthening the dominated convergence theorem via uniform integrability.
• E. Dirichlet theorem on Fourier series
  The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.