See Borel σ-algebra in All languages combined, or Wiktionary
{ "etymology_templates": [ { "args": { "1": "mathematician", "2": "", "3": "", "4": "", "5": "" }, "expansion": "mathematician", "name": "named-after/list" }, { "args": {}, "expansion": "|", "name": "!" }, { "args": { "1": "en", "2": "Émile Borel" }, "expansion": "Émile Borel", "name": "lang" }, { "args": { "1": "en", "2": "Émile Borel", "born": "1871", "died": "1956", "nat": "French", "occ": "mathematician", "wplink": "=" }, "expansion": "Named after French mathematician Émile Borel (1871–1956)", "name": "named-after" } ], "etymology_text": "Named after French mathematician Émile Borel (1871–1956), who pioneered measure theory.", "forms": [ { "form": "Borel σ-algebras", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "Borel σ-algebras", "head": "Borel σ-algebra" }, "expansion": "Borel σ-algebra (plural Borel σ-algebras)", "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": "English terms containing italics", "parents": [ "Terms containing italics", "Terms by orthographic property", "Terms by lexical property" ], "source": "w" }, { "kind": "other", "name": "English terms written in multiple scripts", "parents": [ "Terms written in multiple scripts", "Terms by orthographic property", "Terms by lexical property" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with DISPLAYTITLE conflicts", "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 French 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" } ], "glosses": [ "The smallest σ-algebra which contains the topology of a given topological space." ], "hypernyms": [ { "word": "σ-algebra" } ], "id": "en-Borel_σ-algebra-en-noun-DUwDWZgk", "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "σ-algebra", "σ-algebra" ], [ "topology", "topology" ], [ "topological space", "topological space" ] ], "meronyms": [ { "word": "Borel set" }, { "word": "topology" } ], "raw_glosses": [ "(mathematical analysis) The smallest σ-algebra which contains the topology of a given topological space." ], "related": [ { "word": "Borel measure" } ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "Translations", "word": "Borelin sigma-algebra" }, { "code": "fr", "lang": "French", "sense": "Translations", "tags": [ "feminine" ], "word": "tribu borélienne" }, { "code": "de", "lang": "German", "sense": "Translations", "tags": [ "feminine" ], "word": "Borel-σ-Algebra" }, { "code": "de", "lang": "German", "sense": "Translations", "tags": [ "feminine" ], "word": "borelsche σ-Algebra" }, { "code": "pl", "lang": "Polish", "sense": "Translations", "tags": [ "feminine" ], "word": "σ-algebra borelowska" } ], "wikipedia": [ "Borel σ-algebra" ] } ], "word": "Borel σ-algebra" }
{ "etymology_templates": [ { "args": { "1": "mathematician", "2": "", "3": "", "4": "", "5": "" }, "expansion": "mathematician", "name": "named-after/list" }, { "args": {}, "expansion": "|", "name": "!" }, { "args": { "1": "en", "2": "Émile Borel" }, "expansion": "Émile Borel", "name": "lang" }, { "args": { "1": "en", "2": "Émile Borel", "born": "1871", "died": "1956", "nat": "French", "occ": "mathematician", "wplink": "=" }, "expansion": "Named after French mathematician Émile Borel (1871–1956)", "name": "named-after" } ], "etymology_text": "Named after French mathematician Émile Borel (1871–1956), who pioneered measure theory.", "forms": [ { "form": "Borel σ-algebras", "tags": [ "plural" ] } ], "head_templates": [ { "args": { "1": "Borel σ-algebras", "head": "Borel σ-algebra" }, "expansion": "Borel σ-algebra (plural Borel σ-algebras)", "name": "en-noun" } ], "hypernyms": [ { "word": "σ-algebra" } ], "lang": "English", "lang_code": "en", "meronyms": [ { "word": "Borel set" }, { "word": "topology" } ], "pos": "noun", "related": [ { "word": "Borel measure" } ], "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English nouns", "English terms containing italics", "English terms spelled with Σ", "English terms written in multiple scripts", "Entries with translation boxes", "Pages with 1 entry", "Pages with DISPLAYTITLE conflicts", "Pages with entries", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Polish translations", "Translation table header lacks gloss", "en:Mathematical analysis", "en:Measure theory" ], "glosses": [ "The smallest σ-algebra which contains the topology of a given topological space." ], "links": [ [ "mathematical analysis", "mathematical analysis" ], [ "σ-algebra", "σ-algebra" ], [ "topology", "topology" ], [ "topological space", "topological space" ] ], "raw_glosses": [ "(mathematical analysis) The smallest σ-algebra which contains the topology of a given topological space." ], "topics": [ "mathematical-analysis", "mathematics", "sciences" ], "wikipedia": [ "Borel σ-algebra" ] } ], "translations": [ { "code": "fi", "lang": "Finnish", "sense": "Translations", "word": "Borelin sigma-algebra" }, { "code": "fr", "lang": "French", "sense": "Translations", "tags": [ "feminine" ], "word": "tribu borélienne" }, { "code": "de", "lang": "German", "sense": "Translations", "tags": [ "feminine" ], "word": "Borel-σ-Algebra" }, { "code": "de", "lang": "German", "sense": "Translations", "tags": [ "feminine" ], "word": "borelsche σ-Algebra" }, { "code": "pl", "lang": "Polish", "sense": "Translations", "tags": [ "feminine" ], "word": "σ-algebra borelowska" } ], "word": "Borel σ-algebra" }
Download raw JSONL data for Borel σ-algebra meaning in English (2.7kB)
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-03-23 from the enwiktionary dump dated 2025-03-21 using wiktextract (fef8596 and 633533e). 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.