Triple

T16619251
Position Surface form Disambiguated ID Type / Status
Subject Edward Marczewski E403777 entity
Predicate hasContribution P477 FINISHED
Object Marczewski measure
The Marczewski measure is a concept in measure theory that generalizes classical measures to study the size and structure of sets, particularly in relation to category and descriptive set theory.
E1223947 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: Marczewski measure | Statement: [Edward Marczewski, hasContribution, Marczewski measure]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Marczewski measure
Context triple: [Edward Marczewski, hasContribution, Marczewski measure]
  • A. 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.
  • B. 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.
  • C. Radon measure
    A Radon measure is a type of measure on a topological space that is locally finite and inner regular, playing a central role in modern measure theory and integration.
  • D. 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.
  • E. 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.
  • 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: Marczewski measure
Triple: [Edward Marczewski, hasContribution, Marczewski measure]
Generated description
The Marczewski measure is a concept in measure theory that generalizes classical measures to study the size and structure of sets, particularly in relation to category and descriptive set theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Marczewski measure
Target entity description: The Marczewski measure is a concept in measure theory that generalizes classical measures to study the size and structure of sets, particularly in relation to category and descriptive set theory.
  • A. 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.
  • B. 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.
  • C. Radon measure
    A Radon measure is a type of measure on a topological space that is locally finite and inner regular, playing a central role in modern measure theory and integration.
  • D. 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.
  • E. 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.
  • 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_69d883897eb481909eaaa088ba9918d9 completed April 10, 2026, 4:58 a.m.
NER Named-entity recognition batch_69e3754c934c8190a0a8ddd747681aa7 completed April 18, 2026, 12:13 p.m.
NED1 Entity disambiguation (via context triple) batch_6a007db0b4348190beb573bc3df98125 completed May 10, 2026, 12:44 p.m.
NEDg Description generation batch_6a007e6507208190b3f32c05a2f647bd completed May 10, 2026, 12:47 p.m.
NED2 Entity disambiguation (via description) batch_6a007f2cefa081908734a907da33a72f completed May 10, 2026, 12:50 p.m.
Created at: April 10, 2026, 5:17 a.m.