Outer measure
In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures. Carathéodory's work on outer measures found many applications in measure-theoretic set theory (outer measures are for example used in the proof of the fundamental Carathéodory's extension theorem), and was used in an essential way by Hausdorff to define a dimension-like metric invariant now called Hausdorff dimension. Outer measures are commonly used in the field of geometric measure theory.
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Caratheodory's measureCaratheodory's theorem (measure theory)Caratheodory measureCaratheodory theorem (measure theory)Carathéodory's measureCarathéodory's theorem (measure theory)Carathéodory-measurable setCarathéodory measureCarathéodory theorem (measure theory)Exterior measureLebesgue outer measure
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Borel regular measureCaratheodory's measureCaratheodory's theorem (measure theory)Caratheodory measureCaratheodory theorem (measure theory)Carathéodory's criterionCarathéodory's extension theoremCarathéodory's measureCarathéodory's theorem (measure theory)Carathéodory-measurable setCarathéodory measureCarathéodory theorem (measure theory)Complete measureConstantin CarathéodoryContent (measure theory)Exterior measureHam sandwich theoremHausdorff measureInner measureLebesgue measureLebesgue outer measureLebesgue–Stieltjes integrationList of integration and measure theory topicsList of real analysis topicsList of theoremsLittlewood's three principles of real analysisLuzin N propertyMeasurable cardinalMeasure (mathematics)Metric outer measurePre-measureProofs and RefutationsSaturated measureStandard probability space
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Outer measure
In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. The theory of outer measures was first introduced by Constantin Carathéodory to provide an abstract basis for the theory of measurable sets and countably additive measures. Carathéodory's work on outer measures found many applications in measure-theoretic set theory (outer measures are for example used in the proof of the fundamental Carathéodory's extension theorem), and was used in an essential way by Hausdorff to define a dimension-like metric invariant now called Hausdorff dimension. Outer measures are commonly used in the field of geometric measure theory.
has abstract
Em matemática, uma medida exte ...... terior, a medida de Hausdorff.
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In matematica, in particolare ...... tà numerabile sia soddisfatta.
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In the mathematical field of m ...... countable additivity property.
@en
La notion de mesure extérieure ...... esurables de la droite réelle.
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Miara zewnętrzna – monotoniczn ...... nego dziś wymiarem Hausdorffa.
@pl
Una medida exterior sobre un c ...... tir de ellas, una medida en X.
@es
Yttre mått är ett begrepp i må ...... a i själva verket är ett mått.
@sv
В математиці, зокрема в теорії ...... крім інтервалів або ж куль в .
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Внешняя мера — одно из обобщен ...... ительным техническим условиям.
@ru
在数学中，特别是测度论中，外测度是一个定义在给定集合上的扩展 ...... 造外测度的目的就是选出那些可测集合，使得可数可加性得到满足。
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Em matemática, uma medida exte ...... terior, a medida de Hausdorff.
@pt
In matematica, in particolare ...... fa le seguenti tre condizioni:
@it
In the mathematical field of m ...... d of geometric measure theory.
@en
La notion de mesure extérieure ...... esurables de la droite réelle.
@fr
Miara zewnętrzna – monotoniczn ...... iedy miarami Carathéodory’ego.
@pl
Una medida exterior sobre un c ...... tir de ellas, una medida en X.
@es
Yttre mått är ett begrepp i må ...... a i själva verket är ett mått.
@sv
В математиці, зокрема в теорії ...... ться Гаусдорфовою розмірністю.
@uk
Внешняя мера — одно из обобщен ...... ительным техническим условиям.
@ru
在数学中，特别是测度论中，外测度是一个定义在给定集合上的扩展 ...... 造外测度的目的就是选出那些可测集合，使得可数可加性得到满足。
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label
Medida exterior
@es
Medida exterior
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Mesure extérieure
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Miara zewnętrzna
@pl
Misura esterna
@it
Outer measure
@en
Yttre mått
@sv
Äußeres Maß
@de
Внешняя мера
@ru
Зовнішня міра
@uk