| dbo:abstract
|
- In mathematics, the Kuratowski–Ulam theorem, introduced by Kazimierz Kuratowski and Stanislaw Ulam, called also the Fubini theorem for category, is an analog of Fubini's theorem for arbitrary second countable Baire spaces. Let X and Y be second countable Baire spaces (or, in particular, Polish spaces), and let . Then the following are equivalent if A has the Baire property: 1.
* A is meager (respectively comeager). 2.
* The set is comeager in X, where , where is the projection onto Y. Even if A does not have the Baire property, 2. follows from 1.Note that the theorem still holds (perhaps vacuously) for X an arbitrary Hausdorff space and Y a Hausdorff space with countable π-base. The theorem is analogous to the regular Fubini's theorem for the case where the considered function is a characteristic function of a subset in a product space, with the usual correspondences, namely, meagre set with a set of measure zero, comeagre set with one of full measure, and a set with the Baire property with a measurable set. (en)
|
| dbo:wikiPageExternalLink
| |
| dbo:wikiPageID
| |
| dbo:wikiPageLength
|
- 2600 (xsd:nonNegativeInteger)
|
| dbo:wikiPageRevisionID
| |
| dbo:wikiPageWikiLink
| |
| dbp:author1Link
|
- Kazimierz Kuratowski (en)
|
| dbp:author2Link
| |
| dbp:first
|
- Stanislaw (en)
- Kazimierz (en)
|
| dbp:last
|
- Kuratowski (en)
- Ulam (en)
|
| dbp:wikiPageUsesTemplate
| |
| dbp:year
| |
| dcterms:subject
| |
| rdfs:comment
|
- In mathematics, the Kuratowski–Ulam theorem, introduced by Kazimierz Kuratowski and Stanislaw Ulam, called also the Fubini theorem for category, is an analog of Fubini's theorem for arbitrary second countable Baire spaces. Let X and Y be second countable Baire spaces (or, in particular, Polish spaces), and let . Then the following are equivalent if A has the Baire property: 1.
* A is meager (respectively comeager). 2.
* The set is comeager in X, where , where is the projection onto Y. (en)
|
| rdfs:label
|
- Kuratowski–Ulam theorem (en)
|
| owl:sameAs
| |
| prov:wasDerivedFrom
| |
| foaf:isPrimaryTopicOf
| |
| is dbo:wikiPageRedirects
of | |
| is dbo:wikiPageWikiLink
of | |
| is foaf:primaryTopic
of | |
