The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping
We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in c...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202110337 |
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| _version_ | 1832564693605023744 |
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| author | Hongwen Guo Dihe Hu |
| author_facet | Hongwen Guo Dihe Hu |
| author_sort | Hongwen Guo |
| collection | DOAJ |
| description | We weaken the open set condition and define a finite intersection
property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results, about random recursive fractals. |
| format | Article |
| id | doaj-art-8743da08993e40d19264e0c9d391abe0 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8743da08993e40d19264e0c9d391abe02025-02-03T01:10:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01311112110.1155/S0161171202110337The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlappingHongwen Guo0Dihe Hu1College of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaCollege of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaWe weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results, about random recursive fractals.http://dx.doi.org/10.1155/S0161171202110337 |
| spellingShingle | Hongwen Guo Dihe Hu The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping International Journal of Mathematics and Mathematical Sciences |
| title | The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping |
| title_full | The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping |
| title_fullStr | The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping |
| title_full_unstemmed | The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping |
| title_short | The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping |
| title_sort | hausdorff dimension and exact hausdorff measure of random recursive sets with overlapping |
| url | http://dx.doi.org/10.1155/S0161171202110337 |
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