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: ergodic theorem | Statement: [law of large numbers, relatesTo, ergodic theorem]

Target entity: ergodic theorem
Context triple: [law of large numbers, relatesTo, ergodic theorem]

• A. 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.
• B. 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.
• C. 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.
• 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. Poincaré recurrence theorem
  The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: ergodic theorem
Triple: [law of large numbers, relatesTo, ergodic theorem]

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.

Target entity: ergodic theorem
Target entity description: 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.

• A. 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.
• B. 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.
• C. 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.
• 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. Poincaré recurrence theorem
  The Poincaré recurrence theorem is a fundamental result in dynamical systems and ergodic theory stating that certain systems will, after a sufficiently long but finite time, return arbitrarily close to their initial state.
• F. None of above. chosen