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Donzellathesis.pdf (268.22 KB)
ETD Abstract Container
Abstract Header
The Geometry of Rectifiable and Unrectifiable Sets
Author Info
Donzella, Michael A
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=kent1404332888
Abstract Details
Year and Degree
2014, MS, Kent State University, College of Arts and Sciences / Department of Mathematical Sciences.
Abstract
In his fundamental work, Besicovitch distinguished two classes of sets, rectifiable and purely unrectifiable. The rectifiable sets form a natural measure theoretic generalization of a smooth curve. The notion of a purely unrectifiable set is a rigorous way to define a set often known as a fractal. In this thesis, many of the fundamental properties of these two classes of sets will be discussed, leading toward a self-contained proof of the Besicovitch-Federer theorem, which provides a necessary and sufficient condition for the unrectifiability of a set in terms of the Hausdorff measure (or length) of its orthogonal projections.
Committee
Benjamin Jaye, Phd (Advisor)
Pages
49 p.
Subject Headings
Mathematics
Keywords
Geometric Measure Theory
;
Hausdorff Measure
;
Rectifiability
;
Unrectifiability
;
Besicovitch Projection Theorem
;
fractals
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Refworks
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Citations
Donzella, M. A. (2014).
The Geometry of Rectifiable and Unrectifiable Sets
[Master's thesis, Kent State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=kent1404332888
APA Style (7th edition)
Donzella, Michael.
The Geometry of Rectifiable and Unrectifiable Sets.
2014. Kent State University, Master's thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=kent1404332888.
MLA Style (8th edition)
Donzella, Michael. "The Geometry of Rectifiable and Unrectifiable Sets." Master's thesis, Kent State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1404332888
Chicago Manual of Style (17th edition)
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Document number:
kent1404332888
Download Count:
1,991
Copyright Info
© 2014, some rights reserved.
The Geometry of Rectifiable and Unrectifiable Sets by Michael A Donzella is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by Kent State University and OhioLINK.