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Josept M. Rosenblatt Ayaragarnchanakul, Jantana C. 2015-09-28T15:19:30Z 2015-09-28T15:19:30Z 10000-01-01 2001 2001 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 . Made available in DSpace on 2015-09-28T15:19:30Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023013.pdf: 3525369 bytes, checksum: 3e8619c9b0f5c336318b08fa47f1dcac (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88064 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 117 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86783 (MiAaPQ)AAI3023013 eng Mathematics Divergence in Ergodic Theory text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.