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: Kolmogorov extension theorem | Statement: [Kolmogorov continuity theorem, relatedTo, Kolmogorov extension theorem]

Target entity: Kolmogorov extension theorem
Context triple: [Kolmogorov continuity theorem, relatedTo, Kolmogorov extension theorem]

• A. Kolmogorov extension theorem chosen
  The Kolmogorov extension theorem is a fundamental result in probability theory that guarantees the existence of a stochastic process with given consistent finite-dimensional distributions.
• B. 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.
• C. Kolmogorov axioms
  The Kolmogorov axioms are the standard mathematical foundation of probability theory, formalizing probabilities as measures on a sigma-algebra that satisfy non-negativity, normalization, and countable additivity.
• D. 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.
• 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.
• G. Unsure - the case is ambiguous/there is not enough information to decide.