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 axioms | Statement: [Probability theory, axiomatizedIn, Kolmogorov axioms]

Target entity: Kolmogorov axioms
Context triple: [Probability theory, axiomatizedIn, Kolmogorov axioms]

• A. Kolmogorov axioms chosen
  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.
• 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. Kolmogorov extension theorem
  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.
• D. Shannon–Khinchin axioms
  The Shannon–Khinchin axioms are a set of fundamental conditions that uniquely characterize Shannon entropy as the standard measure of information and uncertainty in probability theory and information theory.
• E. 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.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: axiomatizedIn
Context triple: [Probability theory, axiomatizedIn, Kolmogorov axioms]

• A. axiom2
  Indicates that the relationship or action is taken as a fundamental, assumed truth within the system, serving as a base rule from which other statements are derived.
• B. hasAxiom chosen
  Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
• C. foundationAxiomHoldsIn
  Indicates that the foundation (or regularity) axiom is satisfied within a given model, structure, or context.
• D. isFormalizedBy
  Indicates that something is given a defined, structured, or official form through a specific method, process, or representation.
• E. κατείχεΑξίωμα
  Indicates that an entity held or occupied a particular office or official position.
• F. None of above.