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| has gloss | eng: 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. They appear naturally in harmonic analysis or potential theory. |
| lexicalization | eng: Hausdorff measure |
| instance of | e/Fractal |
| Meaning | |
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| German | |
| lexicalization | deu: Hausdorff-Maß |
| lexicalization | deu: Hausdorffmaß |
| French | |
| lexicalization | fra: Mesure de Hausdorff |
| Dutch | |
| has gloss | nld: De Hausdorffmaat, genoemd naar de Duitse wiskundige Felix Hausdorff, bepaalt de maat (afmeting, volume) van een deelverzameling van de n-dimensionale ruimte \R^n of algemener van een metrische ruimte. |
| lexicalization | nld: Hausdorffmaat |
| Piemontese | |
| has gloss | pms: As definiss la mzura ëd Hausdorff p-dimensional \Lambda^p(S) d'S an butand : \Lambda^p(S)= \sup\\Lambda_ \varepsilon }^p(S) \mid\varepsilon >0 \} = \lim_ \varepsilon\rightarrow 0^+} \Lambda_ \varepsilon }^p(S). |
| lexicalization | pms: Mzura ëd Hausdorff |
| Portuguese | |
| has gloss | por: Em matemática, a medida de Hausdorff é um tipo de medida exterior cujo nome se deve ao matemático alemão Felix Hausdorff e que associa a cada subconjunto do espaço euclidiano \mathbbR}^n um número real estendido não negativo. O conceito pode ser definido para qualquer espaço métrico. |
| lexicalization | por: medida de Hausdorff |
| Russian | |
| has gloss | rus: Мера Хаусдорфа — собирательное название класса мер, определённых на борелевской \sigma-алгебре \mathcalB}(X) метрического пространства X. |
| lexicalization | rus: Мера Хаусдорфа |
| Swedish | |
| has gloss | swe: Ett Hausdorffmått är inom matematik ett mått för metriska rum som är en generalisering av Lebesguemåttet. Hausdorffmåttet är namngett efter Felix Hausdorff som uppfann det. |
| lexicalization | swe: Hausdorffmått |
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