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Meaning of Hausdorff content | Babel Free

Noun CEFR B2

Definitions

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.

Examples

“The d-dimensional Hausdorff content of a set is a measure of the size of that set in the dᵗʰ dimension.”

“The 0-dimensional Hausdorff content of a set is the number of points in that set.”

CEFR level

B2

Upper Intermediate
This word is part of the CEFR B2 vocabulary — upper intermediate level.

See also

Hausdorff dimension Hausdorff distance Hausdorff gap Hausdorff metric Hausdorff space Hausdorffness