About: Negligible set

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In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose.As common examples, finite sets can be ignored when studying the limit of a sequence, and null sets can be ignored when studying the integral of a measurable function. The opposite of a negligible set is a generic property, which has various forms.

Attributes	Values
rdf:type	building
rdfs:label	Insieme trascurabile (it) Negligible set (en)
rdfs:comment	In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose.As common examples, finite sets can be ignored when studying the limit of a sequence, and null sets can be ignored when studying the integral of a measurable function. The opposite of a negligible set is a generic property, which has various forms. (en) In matematica, un insieme trascurabile è un insieme abbastanza piccolo da essere ignorato in determinati casi. Per esempio gli insiemi finiti possono essere ignorati nello studio del limite di una successione, e gli insiemi nulli possono essere ignorati quando si studia l'integrale di una funzione misurabile. (it)
dcterms:subject	Mathematical analysis
Wikipage page ID	195132 (xsd:integer)
Wikipage revision ID	1113787453 (xsd:integer)
Link from a Wikipage to another Wikipage	Almost everywhere Upper bound Infinite set Limit of a sequence Complement (set theory) Countable set Mathematics Measure (mathematics) Generic property Sigma-ideal Dense set Empty set Measurable function Measurable space Countable Lebesgue measure Finite set First category Null set Directed set Mathematical analysis Coarse structure Ideal (set theory) Iff Natural number Net (mathematics) Open set Real number Set (mathematics) Union (set theory) Negligible function Real line Topological space Subset Uncountable set Nowhere-dense set Integral (measure theory)
sameAs	Negligible set Negligible set Negligible set Negligible set
dbp:wikiPageUsesTemplate	dbt:Mvar dbt:Refimprove dbt:Reflist dbt:Short_description
has abstract	In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose.As common examples, finite sets can be ignored when studying the limit of a sequence, and null sets can be ignored when studying the integral of a measurable function. Negligible sets define several useful concepts that can be applied in various situations, such as truth almost everywhere.In order for these to work, it is generally only necessary that the negligible sets form an ideal; that is, that the empty set be negligible, the union of two negligible sets be negligible, and any subset of a negligible set be negligible.For some purposes, we also need this ideal to be a sigma-ideal, so that countable unions of negligible sets are also negligible.If I and J are both ideals of subsets of the same set X, then one may speak of I-negligible and J-negligible subsets. The opposite of a negligible set is a generic property, which has various forms. (en) In matematica, un insieme trascurabile è un insieme abbastanza piccolo da essere ignorato in determinati casi. Per esempio gli insiemi finiti possono essere ignorati nello studio del limite di una successione, e gli insiemi nulli possono essere ignorati quando si studia l'integrale di una funzione misurabile. Gli insiemi trascurabili definiscono molti concetti utili che possono essere applicati in varie situazioni, come la nozione di vero quasi ovunque. Perché tutto questo funzioni, in genere è sufficiente che gli insiemi trascurabili formino un ideale; cioè, che l'insieme vuoto sia trascurabile, l'unione di due insiemi trascurabili sia trascurabile, e che ogni sottoinsieme di un insieme trascurabile sia trascurabile. In alcuni casi è necessario anche che l'ideale sia un , in modo che l'unione numerabile di insiemi trascurabili sia ancora trascurabile. Se I e J sono ideali di sottoinsiemi dello stesso insieme X, allora si può parlare di sottoinsiemi I-trascurabili e J-trascurabili. (it)
gold:hypernym	Property
prov:wasDerivedFrom	wikipedia-en:Negligible_set?oldid=1113787453&ns=0
page length (characters) of wiki page	4704 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Negligible_set
is rdfs:seeAlso of	Generic property
is Link from a Wikipage to another Wikipage of	List of exceptional set concepts Index of combinatorics articles List of integration and measure theory topics Nowhere dense set Generic property Sigma-ideal Meagre set Almost all Null set Dirichlet function Henry John Stephen Smith Coarse structure Negligible function List of types of sets Evolutionary invasion analysis Polar set (potential theory)
is foaf:primaryTopic of	wikipedia-en:Negligible_set

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