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Descriptive Properties of Measure Preserving Actions and the Associated Unitary Representations


Wei, Tzer-jen (2005) Descriptive Properties of Measure Preserving Actions and the Associated Unitary Representations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/HECM-A179.


This thesis consists of two independent parts.

In the first part, we study the descriptive complexity of full groups [E]. The main result is
i) If E is not smooth, then [E] is Sigma⁰₃3 complete;
ii) If E is smooth, then [E] is closed.

In the second part, we study descriptive properties of the Koopman unitary repreesentation associated with the measure preserving action. We characterize the smoothness and compressibility of the equivalence induced by the unitary representaion. We also study many connections between the equivalence relation on L^2(X) and the equivalence relation on X.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:descriptive set theory; ergodic Theory; unitary representations
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)
  • Wales, David B.
  • Makarov, Nikolai G.
Defense Date:12 May 2005
Record Number:CaltechETD:etd-05202005-160741
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1896
Deposited By: Imported from ETD-db
Deposited On:23 May 2005
Last Modified:22 May 2020 22:11

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