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Some topics in descriptive set theory and analysis

Citation

Ramsamujh, Taje Indrallal (1986) Some topics in descriptive set theory and analysis. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:01202017-145315777

Abstract

Coanalytic subsets of some well known Polish spaces are investigated. A natural norm (rank function) on each subset is defined and studied by using well-founded trees and transfinite induction as the main tools. The norm provides a natural measure of the complexity of the elements in each subset. It also provides a "Rank Argument" of the non-Borelness of the subset.

The work is divided into four chapters. In Chapter 1 nowhere differentiable continuous functions and Besicovitch functions are studied. Chapter 2 deals with functions with everywhere divergent Fourier series, and everywhere divergent trigonometric series with coefficients that tend to zero. Compact Jordan sets (i.e., sets without cavities) and compact simply-connected sets in the plane are investigated in Chapter 3. Chapter 4 is a miscellany of results extending earlier work of M. Ajtai, A. Kechris and H. Woodin on differentiable functions and continuous functions with everywhere convergent Fourier series.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Kechris, Alexander S.
Thesis Committee:
  • Unknown, Unknown
Defense Date:5 May 1986
Funders:
Funding AgencyGrant Number
CaltechUNSPECIFIED
Record Number:CaltechTHESIS:01202017-145315777
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:01202017-145315777
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10017
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:20 Jan 2017 23:41
Last Modified:20 Jan 2017 23:41

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