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 Title: Pointwise Relations Between Ergodic Averages and Martingales Author(s): Goubran, Nader Doctoral Committee Chair(s): Rosenblatt, Joseph Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: It is known that the ergodic averages An 4 , in the context of the shift action on Z , satisfy pointwise inequalities of the form An4≤CE4 &vbm0;Fn+E4 &vbm0;Gn , where {Fn}n ≥ 1 and {Gn} n ≥ 1 are decreasing sequences of sigma-algebras on Z . In this thesis we extend this by examining situations when the ergodic averages can be pointwise dominated by one reversed martingale, situations when a reversed martingale can be pointwise dominated by ergodic averages, and when differentiation averages can be dominated by a martingale. Issue Date: 2002 Type: Text Language: English Description: 51 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002. URI: http://hdl.handle.net/2142/86799 Other Identifier(s): (MiAaPQ)AAI3070310 Date Available in IDEALS: 2015-09-28 Date Deposited: 2002
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