Triple

T16474962
Position Surface form Disambiguated ID Type / Status
Subject measure theory E400163 entity
Predicate usesConcept P531 FINISHED
Object dominated convergence theorem E284672 NE FINISHED

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: dominated convergence theorem | Statement: [measure theory, usesConcept, dominated convergence theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: dominated convergence theorem
Context triple: [measure theory, usesConcept, dominated convergence theorem]
  • A. dominated convergence theorem chosen
    The dominated convergence theorem is a fundamental result in measure theory that provides conditions under which one can interchange limits and integrals for sequences of functions bounded by an integrable dominating function.
  • B. Vitali convergence theorem
    The Vitali convergence theorem is a result in measure theory that gives conditions under which pointwise convergence of a sequence of integrable functions implies convergence of their integrals, strengthening the dominated convergence theorem via uniform integrability.
  • C. monotone convergence theorem
    The monotone convergence theorem is a fundamental result in measure theory stating that the integral of a pointwise increasing sequence of nonnegative measurable functions equals the limit of their integrals.
  • D. 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.
  • E. Fatou's lemma
    Fatou's lemma is a fundamental result in measure theory that provides an inequality relating the integral of the pointwise limit inferior of a sequence of nonnegative measurable functions to the limit inferior of their integrals.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d883813098819084f5409539723b59 completed April 10, 2026, 4:58 a.m.
NER Named-entity recognition batch_69e32dd43cf88190881a5cbc80da1490 completed April 18, 2026, 7:08 a.m.
NED1 Entity disambiguation (via context triple) batch_6a004f5f238881909b5f2fb41da3f932 completed May 10, 2026, 9:26 a.m.
Created at: April 10, 2026, 5:13 a.m.