Triple

T27133647
Position Surface form Disambiguated ID Type / Status
Subject Borel set E681623 entity
Predicate relationToLebesgueMeasurable P121125 FINISHED
Object every Borel set in ℝ is Lebesgue measurable LITERAL 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: every Borel set in ℝ is Lebesgue measurable | Statement: [Borel set, relationToLebesgueMeasurable, every Borel set in ℝ is Lebesgue measurable]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: relationToLebesgueMeasurable
Context triple: [Borel set, relationToLebesgueMeasurable, every Borel set in ℝ is Lebesgue measurable]
  • A. hasLebesgueMeasure
    Indicates that a set is assigned a specific value by the Lebesgue measure, representing its "size" in the sense of measure theory.
  • B. impliesUnderMeasurability chosen
    Indicates that one property or condition guarantees that another property or condition is measurable (in the measure-theoretic sense).
  • C. isAbsolutelyContinuousWithRespectTo
    Indicates that one measure changes in such a way that it assigns zero measure to every set that another reference measure also considers negligible.
  • D. hasNonMeasurableSets
    Indicates that within a given set or space, there exist subsets that are not measurable under the specified measure or sigma-algebra.
  • E. measurability
    Indicates that a quantity, property, or outcome can be defined, quantified, or assessed using a consistent measurement framework.
  • F. None of above.

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_69eefacbcc2081909ebf00daa23f1981 completed April 27, 2026, 5:57 a.m.
NER Named-entity recognition batch_69ff46afe7e481908f2862ed11c88db2 completed May 9, 2026, 2:37 p.m.
PD Predicate disambiguation batch_69ff45e9151881909c444a655e852165 completed May 9, 2026, 2:34 p.m.
Created at: April 27, 2026, 9:05 a.m.