See Borel set on Wiktionary
{
"etymology_text": "Named after Émile Borel.",
"forms": [
{
"form": "Borel sets",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Borel set (plural Borel sets)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
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},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Polish translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Measure theory",
"orig": "en:Measure theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "A Lebesgue measurable set is expressible as a union of a Borel set and a Lebesgue null set.",
"type": "example"
}
],
"glosses": [
"Any of the members of a Borel σ-algebra."
],
"holonyms": [
{
"word": "Borel σ-algebra"
}
],
"hyponyms": [
{
"word": "Fσ"
},
{
"word": "Gδ"
}
],
"id": "en-Borel_set-en-noun-9dNeCZHO",
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"Borel σ-algebra",
"Borel σ-algebra"
]
],
"raw_glosses": [
"(mathematical analysis) Any of the members of a Borel σ-algebra."
],
"related": [
{
"word": "borelian"
}
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "Borel-joukko"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"feminine"
],
"word": "Borel-Menge"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"feminine"
],
"word": "Borelsche Menge"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "zbiór borelowski"
}
],
"wikipedia": [
"Borel set",
"Émile Borel"
]
}
],
"word": "Borel set"
}
{
"etymology_text": "Named after Émile Borel.",
"forms": [
{
"form": "Borel sets",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Borel set (plural Borel sets)",
"name": "en-noun"
}
],
"holonyms": [
{
"word": "Borel σ-algebra"
}
],
"hyponyms": [
{
"word": "Fσ"
},
{
"word": "Gδ"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "borelian"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with usage examples",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with Finnish translations",
"Terms with German translations",
"Terms with Polish translations",
"Translation table header lacks gloss",
"en:Mathematical analysis",
"en:Measure theory"
],
"examples": [
{
"text": "A Lebesgue measurable set is expressible as a union of a Borel set and a Lebesgue null set.",
"type": "example"
}
],
"glosses": [
"Any of the members of a Borel σ-algebra."
],
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"Borel σ-algebra",
"Borel σ-algebra"
]
],
"raw_glosses": [
"(mathematical analysis) Any of the members of a Borel σ-algebra."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
],
"wikipedia": [
"Borel set",
"Émile Borel"
]
}
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "Borel-joukko"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"feminine"
],
"word": "Borel-Menge"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"feminine"
],
"word": "Borelsche Menge"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"tags": [
"masculine"
],
"word": "zbiór borelowski"
}
],
"word": "Borel set"
}
Download raw JSONL data for Borel set meaning in All languages combined (1.8kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.