Measure and integration Geometric measure theory and fractal measures Concept
Hausdorff dimension
Summary
Let be a subset of a metric space. Its Hausdorff dimension is the exponent at which the -dimensional Hausdorff measure of jumps from infinity to zero. It is a real number, not always an integer. It agrees with the usual dimension for smooth curves, surfaces and open sets, and it gives fractals such as the Cantor set non-integer dimensions.
Where this leads
10 pages build on this one.
Further reading
About this page
| Tag | SSNFTHZ6YJ |
|---|---|
| URI | m2://SSNFTHZ6YJ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A78, 28A80 |
| Same as |
Markdown · JSON · Edit on GitHub
What this page needs for W1
- a source with a locator (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Results about this
Used by
- Capacity and Hausdorff dimension
- Apollonian gasket
- Almgren–Pitts min-max theory
- Makarov's theorem on harmonic measure
- Minkowski–Bouligand dimension
- Frostman lemma
- Mandelbrot set
- Almgren's regularity theorem
- Strange attractor
- Bourgain's dimension bound for harmonic measure