Bradley M. Appelhans, PhD, [email protected] 5 Stephanie L. Fitzpatrick, PhD, [email protected] 6 Hong Li, PhD, [email protected] 7 Vernon Cail, MPH, MPA, [email protected] 8 Department of Preventive Medicine, Rush University Medical Center, Chicago, IL 9 10 Molly E. Waring, PhD, [email protected] 11 Department of Quantitative Health Sciences, University of Massach...

The set A is low for (Martin-Löf) randomness if each random set is already random relative to A. A is K-trivial if the prefix complexity K of each initial segment of A is minimal, namely ∀n K(A!n)"K(n) + O(1). We show that these classes coincide. This answers a question of Ambos-Spies and Kučera in: P. Cholak, S. Lempp, M. Lerman, R. Shore, (Eds.), Computability Theory and Its Applications: Cur...