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: Lebesgue measure theory | Statement: [Baire category theorem, contrastsWith, Lebesgue measure theory]

Target entity: Lebesgue measure theory
Context triple: [Baire category theorem, contrastsWith, Lebesgue measure theory]

• A. Lebesgue measure chosen
  Lebesgue measure is the standard way of assigning a consistent notion of "length," "area," or "volume" to subsets of Euclidean space, forming the foundation of modern measure theory and integration.
• B. measure theory
  Measure theory is a branch of mathematical analysis that rigorously formalizes the concepts of length, area, volume, and integration for very general sets and functions.
• C. Lebesgue integration
  Lebesgue integration is a foundational measure-theoretic framework for defining and analyzing integrals, particularly suited to handling limits, convergence, and more general functions than those allowed by Riemann integration.
• D. Lebesgue outer measure
  Lebesgue outer measure is a fundamental set function in real analysis that assigns a nonnegative extended real number to every subset of Euclidean space, serving as the basis for defining Lebesgue measure and measurable sets.
• E. Lebesgue measurable set
  A Lebesgue measurable set is a subset of Euclidean space for which a consistent, translation-invariant notion of "size" (Lebesgue measure) can be assigned, forming the foundation of modern measure theory and integration.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.