[35] Show that there exists an infinite binary sequence which is not random in the sense of Martin-Lof with respect to any computable measure.

[35] Show that there exists an infinite binary sequence ω which is not random in the sense of Martin-L¨of with respect to any computable measure.

Comments. Source: [A.K. Zvonkin and L.A. Levin, Russ. Math. Surveys, 25:6(1970), 83–124]. Hint: Use a computably enumerable set whose characteristic sequence is not random with respect to any computable measure.