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.