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Hausdorff dimensions

Hausdorff dimensions is the plural of Hausdorff dimension.

Meaning of Hausdorff dimension

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...

Questions about Hausdorff dimensions

What is Hausdorff dimensions the plural of?
Hausdorff dimensions is the plural of Hausdorff dimension.

Words near Hausdorff dimensions in the dictionary

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

Source and license

Adapted from Wiktionary: Hausdorff dimensions (page history and authors); 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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