Triple

T18479762
Position Surface form Disambiguated ID Type / Status
Subject Lebesgue differentiation theorem E451526 entity
Predicate relatedTo P37 FINISHED
Object Radon–Nikodym theorem — 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: Radon–Nikodym theorem | Statement: [Lebesgue differentiation theorem, relatedTo, Radon–Nikodym theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Radon–Nikodym theorem
Context triple: [Lebesgue differentiation theorem, relatedTo, Radon–Nikodym theorem]
  • A. Radon–Nikodym derivative chosen
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • B. Nikodym convergence theorem
    The Nikodym convergence theorem is a fundamental result in measure theory that generalizes the Lebesgue dominated convergence theorem by characterizing when convergence of integrals holds under weaker conditions on the dominating measures.
  • C. Lebesgue decomposition theorem
    The Lebesgue decomposition theorem is a fundamental result in measure theory that states any σ-finite measure can be uniquely decomposed into a part that is absolutely continuous with respect to another measure and a part that is singular to it.
  • D. Carathéodory’s extension theorem
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • E. Hahn decomposition theorem
    The Hahn decomposition theorem is a fundamental result in measure theory that states any signed measure space can be partitioned into a positive set and a negative set on which the measure is respectively nonnegative and nonpositive.
  • 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.