Phrase guide

Hausdorff dimension

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

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Pronunciation

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1

noun

Meaning 1

A type of fractal dimension, a real-valued measure of a geometric object that assigns 1 to a line segment, 2 to a square and 3 to a cube. Formally, given a metric space X and a subset of X labeled S, the Hausdorff dimension of S is the infimum of all real-valued d for which the d-dimensional Hausdorff content of S is zero.

Definition source: English Wiktionary via Wiktextract

Topics: mathematical-analysis, mathematics, sciences

Examples

  • If S is nonempty then if the d-dimensional Hausdorff content of S is zero then d is larger than the Hausdorff dimension of S, and if the d-dimensional Hausdorff content of S is infinite then d is smaller or equal to the Hausdorff dimension of S. If the d-dimensional Hausdorff content of S is finite and positive then d is equal to the Hausdorff dimension of S.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

Introduced in 1918 by mathematician Felix Hausdorff.

Across languages

Translations

9 source translations are retained for this English entry.

  • Chinese Mandarin: 豪斯多夫維數 /豪斯多夫维数 (Háosīduōfū wéishù) — type of fractal dimension
  • Czech: Hausdorffova dimenze — type of fractal dimension
  • Finnish: Hausdorffin dimensio — type of fractal dimension
  • French: dimension de Hausdorff — type of fractal dimension
  • Greek: διάσταση Χάουσντορφ (diástasi Cháousntorf) — type of fractal dimension
  • Japanese: ハウスドルフ次元 (Hausudorufu jigen) — type of fractal dimension
  • Korean: 하우스도르프 차원 (hauseudoreupeu chawon) — type of fractal dimension
  • Russian: разме́рность Хаусдорфа (razmérnostʹ Xausdorfa) — type of fractal dimension
  • Spanish: dimensión de Hausdorff — type of fractal dimension