Last Updated
：2025/11/24
Hausdorff content
Noun
Japanese Meaning
Hausdorff content（ハウスドルフ内容）とは、集合 S に対して、その d 次元のハウスドルフ内容 C_Hᵈ(S) を、S を正の半径を持つボールで覆うすべての被覆の下で、各ボールの半径の d 乗の和の下限（infimum）の、各被覆のボール半径が 0 に収束する際の上極限（limsup）で定義される量として与える測度の一種である。
（ plural ）
Quizzes for review
the d-dimensional Hausdorff content of S is defined by C_Hᵈ(S):= lim _(sup ᵢr_i→0) inf Bigl ∑ᵢr_iᵈ:thereisacoverofSbyballswithradiir_i>0 Bigr.
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Hausdorff content
To estimate the fractal dimension of the set, we computed its Hausdorff content for several values of d and observed rapid decay as d increased.
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To estimate the fractal dimension of the set, we computed its Hausdorff content for several values of d and observed rapid decay as d increased.
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