ECCC-Report TR06-038https://eccc.weizmann.ac.il/report/2006/038Comments and Revisions published for TR06-038en-usFri, 17 Mar 2006 05:22:04 +0200
Paper TR06-038
| Finite-State Dimension and Real Arithmetic |
David Doty,
Jack H. Lutz,
Satyadev Nandakumar
https://eccc.weizmann.ac.il/report/2006/038We use entropy rates and Schur concavity to prove that, for every integer k >= 2, every nonzero rational number q, and every real number alpha, the base-k expansions of alpha, q+alpha, and q*alpha all have the same finite-state dimension and the same finite-state strong dimension. This extends, and gives a new proof of, Wall's 1949 theorem stating that the sum or product of a nonzero rational number and a Borel normal number is always Borel normal.
Fri, 17 Mar 2006 05:22:04 +0200https://eccc.weizmann.ac.il/report/2006/038