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.