Im, Mee Seong (2005). Nonstandard approach to Hausdorff measure theory and an analysis of some sets of dimension less than 1. University of Birmingham. M.Phil.
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Im05MPhil.pdf
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Abstract
We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the Hausdorff measure in more detail. We choose to study Hausdorff measure over any other measures since it is well-defined for all sets, and widely used in many different areas in mathematics, physics, probability theory, and so forth.
Finally we generate a particular set and compute its upper and lower Hausdorff dimension. We compare our set with box-counting dimension and other well-known fractal behaviors to analyze the set in a greater detail.
| Type of Work: | Thesis (Masters by Research > M.Phil.) | ||||||
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| Award Type: | Masters by Research > M.Phil. | ||||||
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| College/Faculty: | Schools (1998 to 2008) > School of Mathematics & Statistics | ||||||
| School or Department: | Mathematics and Statistics | ||||||
| Funders: | None/not applicable | ||||||
| Subjects: | Q Science > QA Mathematics | ||||||
| URI: | http://etheses.bham.ac.uk/id/eprint/5218 |
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