Local dimension and regular points
Published online by Cambridge University Press: 24 October 2008
Extract
The Hausdorff–Besicovitch dimension of a set A ⊆ ℝd, denoted dim (A), relates to the structure of A in the neighbourhood of its thickest point. If A is irregular then one may wish for an index which will describe the size of A in different places. The obvious definition of the local dimension of A near x is
and it is not hard to verify that
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 361 - 368
- Copyright
- Copyright © Cambridge Philosophical Society 1992
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