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: Birkhoff ergodic theorem | Statement: [Khinchin–Lévy constant, relatedConcept, Birkhoff ergodic theorem]

Target entity: Birkhoff ergodic theorem
Context triple: [Khinchin–Lévy constant, relatedConcept, Birkhoff ergodic theorem]

• A. ergodic theorem chosen
  The ergodic theorem is a fundamental result in dynamical systems and probability theory that links long-term time averages of a system’s evolution to ensemble or space averages, underpinning the statistical behavior of many physical and stochastic processes.
• B. Kakutani equivalence in ergodic theory
  Kakutani equivalence in ergodic theory is a notion of equivalence between measure-preserving dynamical systems based on the isomorphism of their induced transformations on subsets of positive measure.
• C. Kakutani’s random ergodic theorem
  Kakutani’s random ergodic theorem is a fundamental result in ergodic theory that extends classical ergodic theorems to sequences of randomly chosen measure-preserving transformations.
• D. Khinchin–Kolmogorov theorem
  The Khinchin–Kolmogorov theorem is a fundamental result in probability theory that provides conditions under which series of independent random variables converge almost surely.
• E. Lectures on Ergodic Theory
  "Lectures on Ergodic Theory" is a classic mathematical monograph that systematically develops the foundations and key results of ergodic theory within dynamical systems.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.