Nonstandard approach to Hausdorff measure theory and an analysis of some sets of dimension less than 1

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.

[img]
Preview
Im05MPhil.pdf
PDF - Accepted Version

Download (508kB)

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.)
Award Type: Masters by Research > M.Phil.
Supervisor(s):
Supervisor(s)EmailORCID
Kaye, RichardUNSPECIFIEDUNSPECIFIED
Licence:
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

Actions

Request a Correction Request a Correction
View Item View Item

Downloads

Downloads per month over past year