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 Title: Divergence in Ergodic Theory Author(s): Ayaragarnchanakul, Jantana C. Doctoral Committee Chair(s): Josept M. Rosenblatt Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: Let (X, B , P) be a non-atomic probability space and let T be an invertible measure-preserving transformation of ( X, B , P). Fix a sequence (mk ) in Z and let f ∈ Lp( X), 1 ≤ p ≤ infinity. We know that, depending on what the powers are, the averages 1n k=1nfTmk x may or may not converge a.e. x ∈ X, and they may or may not stay bounded a.e. We consider the properties of sequences (Ln) of real numbers and ( wn) of positive integers so that 1Ln k=1wnf Tmkx and 1Lnsup 1≤k≤n1k j=1k fTmjx converge a.e. x ∈ X for any sequence (mk) in Z . Issue Date: 2001 Type: Text Language: English Description: 117 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. URI: http://hdl.handle.net/2142/86783 Other Identifier(s): (MiAaPQ)AAI3023013 Date Available in IDEALS: 2015-09-28 Date Deposited: 2001
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