Matches in DBpedia 2016-04 for { <http://wikidata.dbpedia.org/resource/Q217357> ?p ?o }
Showing triples 1 to 79 of
79
with 100 triples per page.
- Q217357 subject Q5639957.
- Q217357 subject Q7036100.
- Q217357 subject Q7139261.
- Q217357 subject Q8732951.
- Q217357 abstract "In mathematical analysis and in probability theory, a σ-algebra (also sigma-algebra, σ-field, sigma-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under union or intersection of countably many subsets. The pair (X, Σ) is called a measurable space.A σ-algebra generalises the concept of an algebra of sets, which only needs to be closed under the union or intersection of finitely many subsets.The main use of σ-algebras is in the definition of measures; specifically, the collection of those subsets for which a given measure is defined is necessarily a σ-algebra. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities. Also, in probability, σ-algebras are pivotal in the definition of conditional expectation.In statistics, (sub) σ-algebras are needed for a formal mathematical definition of sufficient statistic, particularly when the statistic is a function or a random process and the notion of conditional density is not applicable.If X = {a, b, c, d}, one possible σ-algebra on X is Σ = { ∅, {a, b}, {c, d}, {a, b, c, d} }, where ∅ is the empty set. In general, a finite algebra is always a σ-algebra.If {A1, A2, A3, …} is a countable partition of X then the collection of all unions of sets in the partition (including the empty set) is a σ-algebra.A more useful example is the set of subsets of the real line formed by starting with all open intervals and adding in all countable unions, countable intersections, and relative complements and continuing this process (by transfinite iteration through all countable ordinals) until the relevant closure properties are achieved (a construction known as the Borel hierarchy).".
- Q217357 wikiPageWikiLink Q10565797.
- Q217357 wikiPageWikiLink Q1070472.
- Q217357 wikiPageWikiLink Q1080067.
- Q217357 wikiPageWikiLink Q1099110.
- Q217357 wikiPageWikiLink Q1131116.
- Q217357 wikiPageWikiLink Q11348.
- Q217357 wikiPageWikiLink Q1165112.
- Q217357 wikiPageWikiLink Q1187724.
- Q217357 wikiPageWikiLink Q12483.
- Q217357 wikiPageWikiLink Q12681.
- Q217357 wikiPageWikiLink Q1288707.
- Q217357 wikiPageWikiLink Q12916.
- Q217357 wikiPageWikiLink Q1307734.
- Q217357 wikiPageWikiLink Q1378301.
- Q217357 wikiPageWikiLink Q1387228.
- Q217357 wikiPageWikiLink Q148443.
- Q217357 wikiPageWikiLink Q17295.
- Q217357 wikiPageWikiLink Q173300.
- Q217357 wikiPageWikiLink Q176623.
- Q217357 wikiPageWikiLink Q176737.
- Q217357 wikiPageWikiLink Q177646.
- Q217357 wikiPageWikiLink Q179692.
- Q217357 wikiPageWikiLink Q179899.
- Q217357 wikiPageWikiLink Q180953.
- Q217357 wikiPageWikiLink Q185148.
- Q217357 wikiPageWikiLink Q185359.
- Q217357 wikiPageWikiLink Q185837.
- Q217357 wikiPageWikiLink Q191780.
- Q217357 wikiPageWikiLink Q192276.
- Q217357 wikiPageWikiLink Q1935689.
- Q217357 wikiPageWikiLink Q1948412.
- Q217357 wikiPageWikiLink Q205170.
- Q217357 wikiPageWikiLink Q2064647.
- Q217357 wikiPageWikiLink Q213363.
- Q217357 wikiPageWikiLink Q215382.
- Q217357 wikiPageWikiLink Q217357.
- Q217357 wikiPageWikiLink Q226183.
- Q217357 wikiPageWikiLink Q2300258.
- Q217357 wikiPageWikiLink Q242045.
- Q217357 wikiPageWikiLink Q242767.
- Q217357 wikiPageWikiLink Q257387.
- Q217357 wikiPageWikiLink Q3123369.
- Q217357 wikiPageWikiLink Q320357.
- Q217357 wikiPageWikiLink Q355020.
- Q217357 wikiPageWikiLink Q381060.
- Q217357 wikiPageWikiLink Q386228.
- Q217357 wikiPageWikiLink Q3962249.
- Q217357 wikiPageWikiLink Q467440.
- Q217357 wikiPageWikiLink Q4720939.
- Q217357 wikiPageWikiLink Q516776.
- Q217357 wikiPageWikiLink Q5199271.
- Q217357 wikiPageWikiLink Q527101.
- Q217357 wikiPageWikiLink Q5639957.
- Q217357 wikiPageWikiLink Q578985.
- Q217357 wikiPageWikiLink Q5862903.
- Q217357 wikiPageWikiLink Q5919199.
- Q217357 wikiPageWikiLink Q623472.
- Q217357 wikiPageWikiLink Q6268984.
- Q217357 wikiPageWikiLink Q7036100.
- Q217357 wikiPageWikiLink Q709149.
- Q217357 wikiPageWikiLink Q7139261.
- Q217357 wikiPageWikiLink Q719395.
- Q217357 wikiPageWikiLink Q772232.
- Q217357 wikiPageWikiLink Q7754.
- Q217357 wikiPageWikiLink Q80091.
- Q217357 wikiPageWikiLink Q827230.
- Q217357 wikiPageWikiLink Q840810.
- Q217357 wikiPageWikiLink Q842159.
- Q217357 wikiPageWikiLink Q853831.
- Q217357 wikiPageWikiLink Q860623.
- Q217357 wikiPageWikiLink Q8732951.
- Q217357 wikiPageWikiLink Q893487.
- Q217357 comment "In mathematical analysis and in probability theory, a σ-algebra (also sigma-algebra, σ-field, sigma-field) on a set X is a collection Σ of subsets of X that includes the empty subset, is closed under complement, and is closed under union or intersection of countably many subsets.".
- Q217357 label "Sigma-algebra".