Word.ws English Dictionary

Hausdorff dimension

Hausdorff dimension noun: 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.

Noun

Hausdorff dimension (plural Hausdorff dimensions)

  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.
    • 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...

Forms of Hausdorff dimension

pluralHausdorff dimensions

Origin of Hausdorff dimension

Introduced in 1918 by mathematician Felix Hausdorff.

Questions about Hausdorff dimension

What does Hausdorff dimension mean?
Hausdorff dimension means 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.
What part of speech is Hausdorff dimension?
Hausdorff dimension is a noun.
What is the plural of Hausdorff dimension?
The plural of Hausdorff dimension is Hausdorff dimensions.

Words near Hausdorff dimension in the dictionary

  1. Hauschildt
  2. Hausdoerffer
  3. Hausdorff
  4. Hausdorff content
  5. Hausdorff contents
  6. Hausdorff dimension
  7. Hausdorff dimensions
  8. Hausdorff distance
  9. Hausdorff distances
  10. Hausdorff gap
  11. Hausdorff gaps

Source and license

Adapted from Wiktionary: Hausdorff dimension (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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