Triple

T10388988
Position Surface form Disambiguated ID Type / Status
Subject L’intégration dans les groupes topologiques et ses applications E244840 entity
Predicate topic P261 FINISHED
Object 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.
E860100 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: Haar measure | Statement: [L’intégration dans les groupes topologiques et ses applications, topic, Haar measure]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Haar measure
Context triple: [L’intégration dans les groupes topologiques et ses applications, topic, Haar 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. Hausdorff measure
    Hausdorff measure is a fundamental concept in geometric measure theory that generalizes the notion of length, area, and volume to sets with arbitrary fractal or irregular structure in metric spaces.
  • C. 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.
  • D. measure theory
    Measure theory is a branch of mathematical analysis that rigorously formalizes the concepts of length, area, volume, and integration for very general sets and functions.
  • E. Introduction to Abstract Harmonic Analysis
    Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
  • 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: Haar measure
Triple: [L’intégration dans les groupes topologiques et ses applications, topic, Haar measure]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Haar measure
Target entity description: 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.
  • 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. Hausdorff measure
    Hausdorff measure is a fundamental concept in geometric measure theory that generalizes the notion of length, area, and volume to sets with arbitrary fractal or irregular structure in metric spaces.
  • C. 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.
  • D. measure theory
    Measure theory is a branch of mathematical analysis that rigorously formalizes the concepts of length, area, volume, and integration for very general sets and functions.
  • E. Introduction to Abstract Harmonic Analysis
    Introduction to Abstract Harmonic Analysis is a foundational graduate-level textbook that systematically develops the theory of harmonic analysis on topological groups and related abstract structures.
  • 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_69d381b5116081908d85227bab6d3c0c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9b40dd8819080ac839487020a44 completed April 7, 2026, 11:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69d795b2423c8190a7c0e9b6fcbcc6db completed April 9, 2026, 12:04 p.m.
NEDg Description generation batch_69d7998acbf881909b6f063c4bf2d0a6 completed April 9, 2026, 12:20 p.m.
NED2 Entity disambiguation (via description) batch_69d79aa0cc5481908bc14cda8fb6e8b1 completed April 9, 2026, 12:25 p.m.
Created at: April 6, 2026, 12:05 p.m.