Integer and fractional parts of good averaging sequences in ergodic theory by Michael Boshernitzan 1 Department of Mathematics Rice University Houston, Texas 77251 and Roger L. Jones 2 Department of Mathematics DePaul University 2219 N. Kenmore, Chicago, IL 60614 e-mail: MATRLJ@DePaul.Bitnet and M´ at´ e Wierdl 3 Department of Mathematics Northwestern University Evanston, IL 60201 Abstract. Let p ≥ 1, and let (a k ) be a sequence of real numbers which is a universally good averaging sequence in the sense that for any measure-preserving flow (U t ) t∈IR of a probability space the averages 1 n n X k=1 f (U a k x) converge almost everywhere for f ∈ L p . We show that certain transformations of the sequence (a k ) preserve its good averaging property. In particular, we show that the sequences of integer parts ([[ a k ]]) and fractional parts (hh a k ii) are also good averaging sequences for L p . These results extend work of Bourgain on integer parts of polynomial sequences. 1 Partially supported by NSF Grant 2 Partially supported by NSF Grant 9302012 3 Partially supported by NSF Grant April 28, 2015 1 bosjw5.tex