Singular sets of Lebesgue integrable functions
We discuss the relation of Lebesgue integrability of some functions generated by fractal sets to Minkowski contents and box dimensions of fractals. A Lebesgue integrable function u: R N→ R is constructed which is maximally singular in the sense that the Hausdorff dimension of its singular set is equ...
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| Published in | Chaos, solitons and fractals Vol. 21; no. 5; pp. 1281 - 1287 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2004
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| Online Access | Get full text |
| ISSN | 0960-0779 1873-2887 |
| DOI | 10.1016/j.chaos.2003.12.080 |
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| Summary: | We discuss the relation of Lebesgue integrability of some functions generated by fractal sets to Minkowski contents and box dimensions of fractals. A Lebesgue integrable function
u:
R
N→
R
is constructed which is maximally singular in the sense that the Hausdorff dimension of its singular set is equal to
N. |
|---|---|
| ISSN: | 0960-0779 1873-2887 |
| DOI: | 10.1016/j.chaos.2003.12.080 |