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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. doi:10.7907/8pdn-xf41.


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:Public (worldwide access)
Research Advisor(s):
  • Kechris, Alexander S.
Thesis Committee:
  • Kechris, Alexander S. (chair)
  • Woodin, W. Hugh
  • Wolff, Thomas H.
  • Luxemburg, W. A. J.
  • De Prima, Charles R.
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:14 Jun 2023 23:05

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