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: Bernstein inequality on compact sets | Statement: [Bernstein inequalities, hasVariant, Bernstein inequality on compact sets]

Target entity: Bernstein inequality on compact sets
Context triple: [Bernstein inequalities, hasVariant, Bernstein inequality on compact sets]

• A. Bernstein inequalities chosen
  Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
• B. Markov brothers' inequalities
  Markov brothers' inequalities are classical results in approximation theory that provide upper bounds on the derivatives of polynomials in terms of their degree and maximum absolute value on an interval.
• C. Inequalities for analytic functions
  "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
• D. Hadamard three-circle theorem
  The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
• E. Bernstein theorem
  Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.