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: Banach–Tarski paradox | Statement: [Alfred Tarski, notableWork, Banach–Tarski paradox]

Target entity: Banach–Tarski paradox
Context triple: [Alfred Tarski, notableWork, Banach–Tarski paradox]

• A. Banach–Tarski paradox chosen
  The Banach–Tarski paradox is a theorem in set-theoretic geometry stating that a solid ball in 3‑dimensional space can be decomposed into finitely many non-measurable pieces and reassembled into two identical copies of the original ball, highlighting counterintuitive consequences of the axiom of choice.
• B. Hausdorff paradox
  The Hausdorff paradox is a result in set-theoretic geometry showing that, using the axiom of choice, a sphere can be decomposed into finitely many disjoint pieces that can be reassembled into a set not congruent to the original, illustrating the existence of non-measurable sets and paving the way for the Banach–Tarski paradox.
• C. Mazurkiewicz–Sierpiński paradox
  The Mazurkiewicz–Sierpiński paradox is a result in set-theoretic geometry showing that a sphere can be decomposed and reassembled in a counterintuitive way, illustrating the existence of paradoxical decompositions similar to the Banach–Tarski paradox.
• D. Knaster–Ulam theorem
  The Knaster–Ulam theorem is a result in topology and measure theory that, roughly speaking, guarantees the existence of points with certain symmetry or invariance properties under measure-preserving transformations.
• E. Steinhaus theorem
  The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.