Hausdorff content

noun

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.

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

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

nounHausdorff content (plural Hausdorff contents)

plural Hausdorff contents

  1. 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.

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

    1 more example

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

Cite this entry
APA

Hausdorff content. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Hausdorff%20content

MLA

“Hausdorff content.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Hausdorff%20content. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Hausdorff content,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Hausdorff%20content.

Source: Hausdorff content on Wiktionary, CC BY-SA 4.0.