Triple

T2631481
Position Surface form Disambiguated ID Type / Status
Subject Radon–Nikodym derivative E59639 entity
Predicate relatedTo P37 FINISHED
Object Radon–Nikodym theorem
The Radon–Nikodym theorem is a fundamental result in measure theory that guarantees the existence of a density function relating one σ-finite measure to another that is absolutely continuous with respect to it.
E59639 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: Radon–Nikodym theorem | Statement: [Radon–Nikodym derivative, relatedTo, Radon–Nikodym theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Radon–Nikodym theorem
Context triple: [Radon–Nikodym derivative, relatedTo, Radon–Nikodym theorem]
  • A. Radon–Nikodym derivative
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • B. Carathéodory’s extension theorem
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • C. Tonelli's theorem
    Tonelli's theorem is a fundamental result in measure theory that justifies interchanging the order of integration for non-negative measurable functions in iterated Lebesgue integrals.
  • D. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • E. Girsanov theorem
    Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
  • 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: Radon–Nikodym theorem
Triple: [Radon–Nikodym derivative, relatedTo, Radon–Nikodym theorem]
Generated description
The Radon–Nikodym theorem is a fundamental result in measure theory that guarantees the existence of a density function relating one σ-finite measure to another that is absolutely continuous with respect to it.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Radon–Nikodym theorem
Target entity description: The Radon–Nikodym theorem is a fundamental result in measure theory that guarantees the existence of a density function relating one σ-finite measure to another that is absolutely continuous with respect to it.
  • A. Radon–Nikodym derivative chosen
    The Radon–Nikodym derivative is a function that represents how one measure changes with respect to another absolutely continuous measure, playing a central role in modern probability theory and measure theory.
  • B. Carathéodory’s extension theorem
    Carathéodory’s extension theorem is a fundamental result in measure theory that guarantees a unique extension of a pre-measure defined on an algebra of sets to a complete measure on the generated σ-algebra.
  • C. Tonelli's theorem
    Tonelli's theorem is a fundamental result in measure theory that justifies interchanging the order of integration for non-negative measurable functions in iterated Lebesgue integrals.
  • D. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • E. Girsanov theorem
    Girsanov theorem is a fundamental result in stochastic calculus that describes how the dynamics of stochastic processes, particularly Brownian motion, change under an equivalent change of probability measure.
  • F. None of above.

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_69ab4ac8596c8190b34997e73d9e991c completed March 6, 2026, 9:44 p.m.
NER Named-entity recognition batch_69abd8c6e540819087c7f92432b27b0f completed March 7, 2026, 7:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69af98b93a108190b21f4af3e8c16c2b completed March 10, 2026, 4:06 a.m.
NEDg Description generation batch_69af99f0fac8819084513685f5bc0c34 completed March 10, 2026, 4:11 a.m.
NED2 Entity disambiguation (via description) batch_69af9a71a7848190822e4cfe85fce35c completed March 10, 2026, 4:13 a.m.
Created at: March 6, 2026, 9:50 p.m.