Triple

T18479761
Position Surface form Disambiguated ID Type / Status
Subject Lebesgue differentiation theorem E451526 entity
Predicate generalizationOf P2372 FINISHED
Object Lebesgue density theorem for measurable sets — NE NERFINISHED

How this triple was built (2 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
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).
Input
Phrase: Lebesgue density theorem for measurable sets | Statement: [Lebesgue differentiation theorem, generalizationOf, Lebesgue density theorem for measurable sets]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lebesgue density theorem for measurable sets
Context triple: [Lebesgue differentiation theorem, generalizationOf, Lebesgue density theorem for measurable sets]
  • A. 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.
  • B. Lebesgue measure
    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.
  • C. Lebesgue differentiation theorem chosen
    The Lebesgue differentiation theorem is a fundamental result in real analysis stating that, for an integrable function, the averages over shrinking neighborhoods converge almost everywhere to the function’s pointwise value.
  • D. 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.
  • E. Borel–Lebesgue theorem
    The Borel–Lebesgue theorem is a fundamental result in real analysis and topology that characterizes compact subsets of Euclidean space via the property that every open cover admits a finite subcover.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53066a7108190a50eda9b489c90ca completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.