Triple
T17020275
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Orlicz spaces |
E412928
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Musielak–Orlicz spaces
Musielak–Orlicz spaces are a generalization of Orlicz spaces in functional analysis, where the defining Young function is allowed to vary with the point in the underlying measure space, providing a flexible framework for studying variable growth and integrability conditions.
|
E412928
|
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: Musielak–Orlicz spaces | Statement: [Orlicz spaces, relatedTo, Musielak–Orlicz spaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Musielak–Orlicz spaces Context triple: [Orlicz spaces, relatedTo, Musielak–Orlicz spaces]
-
A.
Orlicz spaces
Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
-
B.
Orlicz–Lorentz spaces
Orlicz–Lorentz spaces are a class of Banach function spaces that combine the growth conditions of Orlicz spaces with the rearrangement-invariant structure of Lorentz spaces, used to generalize and refine classical Lebesgue space theory.
-
C.
Grand Lebesgue spaces
Grand Lebesgue spaces are a class of function spaces that generalize classical Lebesgue and Orlicz spaces by controlling integrability through variable exponents or parameter ranges, making them useful in fine-scale analysis of functions and operators.
-
D.
New classes of Lp-spaces
"New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
-
E.
Orlicz function
An Orlicz function is a convex, increasing function used in functional analysis to generalize the notion of growth conditions in defining Orlicz spaces, extending classical \(L^p\) space theory.
- 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: Musielak–Orlicz spaces Triple: [Orlicz spaces, relatedTo, Musielak–Orlicz spaces]
Generated description
Musielak–Orlicz spaces are a generalization of Orlicz spaces in functional analysis, where the defining Young function is allowed to vary with the point in the underlying measure space, providing a flexible framework for studying variable growth and integrability conditions.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Musielak–Orlicz spaces Target entity description: Musielak–Orlicz spaces are a generalization of Orlicz spaces in functional analysis, where the defining Young function is allowed to vary with the point in the underlying measure space, providing a flexible framework for studying variable growth and integrability conditions.
-
A.
Orlicz spaces
chosen
Orlicz spaces are a class of function spaces that generalize Lebesgue spaces by measuring integrability via convex Orlicz functions rather than fixed power exponents.
-
B.
Orlicz–Lorentz spaces
Orlicz–Lorentz spaces are a class of Banach function spaces that combine the growth conditions of Orlicz spaces with the rearrangement-invariant structure of Lorentz spaces, used to generalize and refine classical Lebesgue space theory.
-
C.
Grand Lebesgue spaces
Grand Lebesgue spaces are a class of function spaces that generalize classical Lebesgue and Orlicz spaces by controlling integrability through variable exponents or parameter ranges, making them useful in fine-scale analysis of functions and operators.
-
D.
New classes of Lp-spaces
"New classes of Lp-spaces" is a mathematical work by Jean Bourgain that introduces and studies novel Banach space structures within the framework of Lp spaces, significantly advancing the theory of functional analysis.
-
E.
Orlicz function
An Orlicz function is a convex, increasing function used in functional analysis to generalize the notion of growth conditions in defining Orlicz spaces, extending classical \(L^p\) space theory.
- 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_69d886cc4170819093deddc7b8b4b6a7 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d482c3a0819099e6ea4acb0a08ee |
completed | April 18, 2026, 6:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a012ed0b78481909a11c1529db6c1cd |
completed | May 11, 2026, 1:20 a.m. |
| NEDg | Description generation | batch_6a012f9339d88190a8976240f5b2a8d8 |
completed | May 11, 2026, 1:23 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a01301a4fbc8190bbd5b5b9bad814d3 |
completed | May 11, 2026, 1:25 a.m. |
Created at: April 10, 2026, 5:33 a.m.