About: Pre-measure

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In mathematics, a pre-measure is a set function that is, in some sense, a precursor to a bona fide measure on a given space. Indeed, one of the fundamental theorems in measure theory states that a pre-measure can be extended to a measure.

Attributes	Values
rdf:type	disease
rdfs:label	Prämaß (de) 前測度 (ja) 준측도 (ko) Pre-measure (en)
rdfs:comment	Ein Prämaß ist eine spezielle Mengenfunktion in der Maßtheorie, die verwendet wird, um den intuitiven Volumenbegriff mathematisch zu präzisieren. Im Gegensatz zu einem Maß muss der Definitionsbereich eines Prämaßes keine σ-Algebra sein. (de) In mathematics, a pre-measure is a set function that is, in some sense, a precursor to a bona fide measure on a given space. Indeed, one of the fundamental theorems in measure theory states that a pre-measure can be extended to a measure. (en) 数学の分野における前測度（ぜんそくど、英: pre-measure）とは、ある意味において、ある与えられた空間上の「真の」測度の前身となる測度である。実際、測度論における基本定理では、すべての前測度は測度へと拡張することができると述べられている。 (ja)
dcterms:subject	Measures (measure theory)
Wikipage page ID	13856372 (xsd:integer)
Wikipage revision ID	1095497199 (xsd:integer)
Link from a Wikipage to another Wikipage	Bona fide Relative complement Ring of sets Countable set Mathematics Measure (mathematics) Measure (mathematics) Sigma-ring Sigma additivity Pairwise disjoint Outer measure Measures (measure theory) Set function Union (set theory) Carathéodory-measurable set
Link from a Wikipage to an external page	https://archive.org/details/realanalysismode00foll https://archive.org/details/realanalysismode00foll/page/n42
sameAs	Pre-measure Pre-measure Pre-measure Pre-measure Pre-measure Pre-measure Pre-measure
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Main dbt:Reflist dbt:MathSciNet dbt:Measure_theory dbt:Families_of_sets
has abstract	Ein Prämaß ist eine spezielle Mengenfunktion in der Maßtheorie, die verwendet wird, um den intuitiven Volumenbegriff mathematisch zu präzisieren. Im Gegensatz zu einem Maß muss der Definitionsbereich eines Prämaßes keine σ-Algebra sein. (de) In mathematics, a pre-measure is a set function that is, in some sense, a precursor to a bona fide measure on a given space. Indeed, one of the fundamental theorems in measure theory states that a pre-measure can be extended to a measure. (en) 数学の分野における前測度（ぜんそくど、英: pre-measure）とは、ある意味において、ある与えられた空間上の「真の」測度の前身となる測度である。実際、測度論における基本定理では、すべての前測度は測度へと拡張することができると述べられている。 (ja)
gold:hypernym	Function
prov:wasDerivedFrom	wikipedia-en:Pre-measure?oldid=1095497199&ns=0
page length (characters) of wiki page	3494 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Pre-measure
is rdfs:seeAlso of	Set function
is Link from a Wikipage to another Wikipage of	Pre-measures Content (measure theory) Carathéodory's extension theorem Packing dimension Set function Premeasure Pre measure
is Wikipage redirect of	Pre-measures Premeasure Pre measure
is foaf:primaryTopic of	wikipedia-en:Pre-measure

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