Citation
Sofronidis, Nikolaos Efstathiou (1999) Topics in descriptive set theory related to equivalence relations, complex borel and analytic sets. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/vva81959. https://resolver.caltech.edu/CaltechTHESIS:01232017134252080
Abstract
The purpose of this doctoral dissertation is first to show that certain kinds of invariants for measures, selfadjoint and unitary operators are as far from complete as possible and second to give new natural examples of complex Borel and analytic sets originating from Analysis and Geometry.
The dissertation is divided in two parts.
In the first part we prove that the measure equivalence relation and certain of its most characteristic subequivalence relations are generically S_{∞} ergodic and unitary conjugacy of selfadjoint and unitary operators is generically turbulent.
In the second part we prove that for any 0 ≤ α < ∞, the set of entire functions whose order is equal to α is ∏^{0}_{3}complete and the set of all sequences of entire functions whose orders converge to α is ∏^{0}_{5}complete. We also prove that given any line in the plane and any cardinal number 1 ≤ n ≤ N_{0}, the set of continuous paths in the plane tracing curves which admit at least n tangents parallel to the given line is Σ^{1}_{1}complete and the set of differentiable paths of class C^{2} in the plane admitting a canonical parameter in [0,1] and tracing curves which have at least n vertices is also Σ^{1}_{1}complete.
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): 
 
Thesis Committee: 
 
Defense Date:  13 April 1999  
Funders: 
 
Record Number:  CaltechTHESIS:01232017134252080  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:01232017134252080  
DOI:  10.7907/vva81959  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  10021  
Collection:  CaltechTHESIS  
Deposited By:  Benjamin Perez  
Deposited On:  23 Jan 2017 22:24  
Last Modified:  16 Apr 2021 22:31 
Thesis Files

PDF
 Final Version
See Usage Policy. 23MB 
Repository Staff Only: item control page