Hausdorff measure
In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in Rn or, more generally, in any metric space. The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite. The one-dimensional Hausdorff measure of a simple curve in Rn is equal to the length of the curve. Likewise, the two dimensional Hausdorff measure of a measurable subset of R2 is proportional to the area of the set. Thus, the concept of the Hausdorff measure generalizes counting, length, and area. It also generalizes volume. In fact, there are d-dimensional Hausdorff measures for any d ≥ 0, which is not necessarily an integer. These measures are fundamental in geometric measure theory. The
Hausdorff measure
In mathematics a Hausdorff measure is a type of outer measure, named for Felix Hausdorff, that assigns a number in [0,∞] to each set in Rn or, more generally, in any metric space. The zero-dimensional Hausdorff measure is the number of points in the set (if the set is finite) or ∞ if the set is infinite. The one-dimensional Hausdorff measure of a simple curve in Rn is equal to the length of the curve. Likewise, the two dimensional Hausdorff measure of a measurable subset of R2 is proportional to the area of the set. Thus, the concept of the Hausdorff measure generalizes counting, length, and area. It also generalizes volume. In fact, there are d-dimensional Hausdorff measures for any d ≥ 0, which is not necessarily an integer. These measures are fundamental in geometric measure theory. The
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De hausdorffmaat, genoemd naar ...... afstand binnen de verzameling:
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Em matemática, a medida de Hau ...... rfície é a medida da sua área.
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En mathématiques, les mesures ...... l’analyse Portail de l’analyse
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In mathematics a Hausdorff mea ...... analysis or potential theory.
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Miara Hausdorffa – rodzaj miar ...... nicznej lub teorii potencjału.
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Zur Bestimmung des Flächeninha ...... härische Maß erläutert werden.
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Мера Хаусдорфа — собирательное ...... ре метрического пространства .
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De hausdorffmaat, genoemd naar ...... le bolletjes gezamenlijk is: ,
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Em matemática, a medida de Hau ...... rico. A medida de Hausdorff em
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En mathématiques, les mesures ...... l’analyse Portail de l’analyse
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In mathematics a Hausdorff mea ...... geometric measure theory. The
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Miara Hausdorffa – rodzaj miar ...... ej teorii miary. Pojawiają się
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Zur Bestimmung des Flächeninha ...... härische Maß erläutert werden.
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Мера Хаусдорфа — собирательное ...... ре метрического пространства .
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label
Hausdorff measure
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Hausdorff-Maß
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Hausdorffmaat
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Medida de Hausdorff
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Mesure de Hausdorff
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Miara Hausdorffa
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Мера Хаусдорфа
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