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 on Euclidean spaces | Statement: [Tonelli's theorem, holdsFor, Lebesgue measure on Euclidean spaces]

Target entity: Lebesgue measure on Euclidean spaces
Context triple: [Tonelli's theorem, holdsFor, Lebesgue measure on Euclidean spaces]

• 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. Carathéodory measurability criterion
  The Carathéodory measurability criterion is a fundamental condition in measure theory that characterizes measurable sets via an outer measure by requiring additivity over intersections and complements.
• C. Lebesgue spaces
  Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
• D. 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.
• E. Hausdorff measure
  Hausdorff measure is a fundamental concept in geometric measure theory that generalizes the notion of length, area, and volume to sets with arbitrary fractal or irregular structure in metric spaces.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.