In mathematics, a rectifiable set is a set that is smooth in a certain measure-theoretic sense. It is an extension of the idea of a rectifiable curve to higher dimensions; loosely speaking, a rectifiable set is a rigorous formulation of a piece-wise smooth set. As such, it has many of the desirable properties of smooth manifolds, including tangent spaces that are defined almost everywhere. Rectifiable sets are the underlying object of study in geometric measure theory.
| Attributes | Values |
|---|
| rdfs:label
| - Rektifizierbare Menge (de)
- Conjunto rectificable (es)
- Ensemble rectifiable (fr)
- 교정 가능 집합 (ko)
- Rectifiable set (en)
- Спрямляемое множество (ru)
|
| rdfs:comment
| - Die Rektifizierbare Menge ist ein zentraler Begriff aus der geometrischen Maßtheorie. Eine solche Menge hat stückweise glatte Eigenschaften und teilt somit fast überall Eigenschaften einer differenzierbarer Mannigfaltigkeit. Insbesondere sind diese Mengen von Bedeutung, weil sie einen approximativen Tangentialraum induzieren. (de)
- Un conjunto rectificable es un conjunto que intuitivamente puede ser aproximado en el entorno de cada punto por un espacio euclídeo. Muchos objetos matemáticos definidos mediante aplicaciones diferenciables son rectificables (también llamados suaves). Mientras que los objetos fractales de aspecto irregular no suelen ser rectificables. (es)
- En mathématiques, un ensemble rectifiable est une généralisation pluridimensionnelle de courbe rectifiable. Ce sont les objets différentiels de la théorie géométrique de la mesure, fondée par Herbert Federer. (fr)
- In mathematics, a rectifiable set is a set that is smooth in a certain measure-theoretic sense. It is an extension of the idea of a rectifiable curve to higher dimensions; loosely speaking, a rectifiable set is a rigorous formulation of a piece-wise smooth set. As such, it has many of the desirable properties of smooth manifolds, including tangent spaces that are defined almost everywhere. Rectifiable sets are the underlying object of study in geometric measure theory. (en)
- 측도론에서, 교정 가능 집합(矯正可能集合, 영어: rectifiable set)은 근사 접공간의 개념을 정의할 수 있는 최소한의 구조를 갖춘, 유클리드 공간 속의 부분 집합이다. (ko)
- Спрямляемое множество — обобщение спрямляемой кривой на высшие размерности. Спрямляемые множества являются основным объектом исследования в геометрической теории меры.На спрямляемые множества обобщается большое число понятий определённых для гладких многообразий.В том числе объёма, касательного пространства, понятие почти всюду и т. д. (ru)
|
| dcterms:subject
| |
| Wikipage page ID
| |
| Wikipage revision ID
| |
| Link from a Wikipage to another Wikipage
| |
| Link from a Wikipage to an external page
| |
| sameAs
| |
| dbp:wikiPageUsesTemplate
| |
| author
| |
| id
| |
| title
| - Geometric measure theory (en)
|
| has abstract
| - Die Rektifizierbare Menge ist ein zentraler Begriff aus der geometrischen Maßtheorie. Eine solche Menge hat stückweise glatte Eigenschaften und teilt somit fast überall Eigenschaften einer differenzierbarer Mannigfaltigkeit. Insbesondere sind diese Mengen von Bedeutung, weil sie einen approximativen Tangentialraum induzieren. (de)
- Un conjunto rectificable es un conjunto que intuitivamente puede ser aproximado en el entorno de cada punto por un espacio euclídeo. Muchos objetos matemáticos definidos mediante aplicaciones diferenciables son rectificables (también llamados suaves). Mientras que los objetos fractales de aspecto irregular no suelen ser rectificables. (es)
- En mathématiques, un ensemble rectifiable est une généralisation pluridimensionnelle de courbe rectifiable. Ce sont les objets différentiels de la théorie géométrique de la mesure, fondée par Herbert Federer. (fr)
- In mathematics, a rectifiable set is a set that is smooth in a certain measure-theoretic sense. It is an extension of the idea of a rectifiable curve to higher dimensions; loosely speaking, a rectifiable set is a rigorous formulation of a piece-wise smooth set. As such, it has many of the desirable properties of smooth manifolds, including tangent spaces that are defined almost everywhere. Rectifiable sets are the underlying object of study in geometric measure theory. (en)
- 측도론에서, 교정 가능 집합(矯正可能集合, 영어: rectifiable set)은 근사 접공간의 개념을 정의할 수 있는 최소한의 구조를 갖춘, 유클리드 공간 속의 부분 집합이다. (ko)
- Спрямляемое множество — обобщение спрямляемой кривой на высшие размерности. Спрямляемые множества являются основным объектом исследования в геометрической теории меры.На спрямляемые множества обобщается большое число понятий определённых для гладких многообразий.В том числе объёма, касательного пространства, понятие почти всюду и т. д. (ru)
|
| prov:wasDerivedFrom
| |
| page length (characters) of wiki page
| |
| foaf:isPrimaryTopicOf
| |
| is Link from a Wikipage to another Wikipage
of | |
| is Wikipage redirect
of | |
| is foaf:primaryTopic
of | |
![[RDF Data]](/fct/images/sw-rdf-blue.png)
![[cxml]](/fct/images/cxml_doc.png)
![[csv]](/fct/images/csv_doc.png)
![[text]](/fct/images/ntriples_doc.png)
![[turtle]](/fct/images/n3turtle_doc.png)
![[ld+json]](/fct/images/jsonld_doc.png)
![[rdf+json]](/fct/images/json_doc.png)
![[rdf+xml]](/fct/images/xml_doc.png)
![[atom+xml]](/fct/images/atom_doc.png)
![[html]](/fct/images/html_doc.png)