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On the Lp-improving property of the Cantor-Lebesgue measure Zhu, Junjie

Abstract

The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets introduced by the German mathematician George Cantor in the late 1800s. Many questions about this set remain unanswered. In this thesis, we study the mapping property of a measure associated with the middle-third Cantor set. Specifically, we study whether the Cantor measure is Lebesgue improving through partly theoretical and partly numerical methods.

Item Metadata

Title
On the Lp-improving property of the Cantor-Lebesgue measure
Creator
Zhu, Junjie
Publisher
University of British Columbia
Date Issued
2020
Description
The middle-third Cantor set is one of the most fundamental examples of self-similar fractal sets introduced by the German mathematician George Cantor in the late 1800s. Many questions about this set remain unanswered. In this thesis, we study the mapping property of a measure associated with the middle-third Cantor set. Specifically, we study whether the Cantor measure is Lebesgue improving through partly theoretical and partly numerical methods.
Genre
Thesis/Dissertation
Type
Text
Language
eng
Date Available
2020-04-24
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0389959
URI
http://hdl.handle.net/2429/74151
Degree (Theses)
Master of Science - MSc
Program (Theses)
Mathematics
Affiliation
Science, Faculty of; Mathematics, Department of
Degree Grantor
University of British Columbia
Graduation Date
2020-05
Campus
UBCV
Scholarly Level
Graduate
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository
DSpace

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Attribution-NonCommercial-NoDerivatives 4.0 International