Triple

T10991499
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Stieltjes integral E259762 entity
Predicate relatedConcept P37 FINISHED
Object Stieltjes measure
A Stieltjes measure is a measure on the real line constructed from a nondecreasing, right-continuous function, providing the measure-theoretic foundation for the Riemann–Stieltjes and Lebesgue–Stieltjes integrals.
E898477 NE FINISHED

How this triple was built (4 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: Stieltjes measure | Statement: [Riemann–Stieltjes integral, relatedConcept, Stieltjes measure]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stieltjes measure
Context triple: [Riemann–Stieltjes integral, relatedConcept, Stieltjes measure]
  • A. 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.
  • B. Wiener measure
    Wiener measure is the canonical probability measure on the space of continuous paths that models standard Brownian motion in probability theory and stochastic analysis.
  • C. 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.
  • D. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • E. Haar measure
    Haar measure is a fundamental concept in harmonic analysis and topological group theory, providing a translation-invariant way to assign measures to subsets of locally compact groups.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Stieltjes measure
Triple: [Riemann–Stieltjes integral, relatedConcept, Stieltjes measure]
Generated description
A Stieltjes measure is a measure on the real line constructed from a nondecreasing, right-continuous function, providing the measure-theoretic foundation for the Riemann–Stieltjes and Lebesgue–Stieltjes integrals.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stieltjes measure
Target entity description: A Stieltjes measure is a measure on the real line constructed from a nondecreasing, right-continuous function, providing the measure-theoretic foundation for the Riemann–Stieltjes and Lebesgue–Stieltjes integrals.
  • A. 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.
  • B. Wiener measure
    Wiener measure is the canonical probability measure on the space of continuous paths that models standard Brownian motion in probability theory and stochastic analysis.
  • C. 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.
  • D. Riemann–Stieltjes integral
    The Riemann–Stieltjes integral is a generalization of the Riemann integral in which integration is taken with respect to a function of bounded variation rather than just the identity function, allowing more flexible treatment of sums and distributions.
  • E. Haar measure
    Haar measure is a fundamental concept in harmonic analysis and topological group theory, providing a translation-invariant way to assign measures to subsets of locally compact groups.
  • F. None of above. chosen

Provenance (5 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.