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: Kac's lemma | Statement: [Poincaré recurrence theorem, relatedConcept, Kac's lemma]

Target entity: Kac's lemma
Context triple: [Poincaré recurrence theorem, relatedConcept, Kac's lemma]

• A. Kronecker’s lemma
  Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
• B. Kolmogorov zero–one law
  The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
• C. Kac walk
  The Kac walk is a probabilistic model introduced by mathematician Mark Kac to study the approach to equilibrium in kinetic theory via a simplified random process.
• D. Kac
  Kac is a surname most notably associated with Polish-American mathematician Mark Kac, known for his work in probability theory and mathematical physics.
• E. 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.
• 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: Kac's lemma
Triple: [Poincaré recurrence theorem, relatedConcept, Kac's lemma]

Kac's lemma is a result in ergodic theory that relates the expected return time to a set in a measure-preserving dynamical system to the inverse of the measure of that set.

Target entity: Kac's lemma
Target entity description: Kac's lemma is a result in ergodic theory that relates the expected return time to a set in a measure-preserving dynamical system to the inverse of the measure of that set.

• A. Kronecker’s lemma
  Kronecker’s lemma is a result in real analysis and summability theory that links the convergence of series with weighted averages of their partial sums, often used in the study of Fourier series and ergodic theorems.
• B. Kolmogorov zero–one law
  The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
• C. Kac walk
  The Kac walk is a probabilistic model introduced by mathematician Mark Kac to study the approach to equilibrium in kinetic theory via a simplified random process.
• D. Kac
  Kac is a surname most notably associated with Polish-American mathematician Mark Kac, known for his work in probability theory and mathematical physics.
• E. 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.
• F. None of above. chosen