Dimension und äußeres Ma߶
Hausdorff, F. (1919). Dimension und äußeres Maß. Mathematische Annalen, 79(1-2), 1-2.
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2 citations across 2 artifacts.
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Primes¶
- Dimension
- and Hilbert's 1891 variant exhibited continuous surjections from ℝ onto ℝ² — objects one-dimensional in parameterization but filling a two-dimensional region — forcing mathematicians to refine "dimension" beyond its naive pre-20-century meaning and preparing the ground for Hausdorff's 1919 definition of fractional dimension
This sourceIntroduces the Hausdorff outer measure and the corresponding non-integer (fractional) dimension; foundational underpinning of fractal geometry, predating Mandelbrot's coinage by half a century.
- and Hilbert's 1891 variant exhibited continuous surjections from ℝ onto ℝ² — objects one-dimensional in parameterization but filling a two-dimensional region — forcing mathematicians to refine "dimension" beyond its naive pre-20-century meaning and preparing the ground for Hausdorff's 1919 definition of fractional dimension
- Fractal Geometry
- 2. Dimension measure: the specific dimension being computed is named — Hausdorff
This sourceOriginal introduction of Hausdorff outer measure and the corresponding non-integer dimension; the canonical (computationally hard) dimension measure cited at D38-154.
- 2. Dimension measure: the specific dimension being computed is named — Hausdorff
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