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Some topics in descriptive set theory and analysis


Ramsamujh, Taje Indrallal (1986) Some topics in descriptive set theory and analysis. Dissertation (Ph.D.), California Institute of Technology.


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
Funding AgencyGrant Number
Record Number:CaltechTHESIS:01202017-145315777
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10017
Deposited By: Benjamin Perez
Deposited On:20 Jan 2017 23:41
Last Modified:20 Jan 2017 23:41

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