[13] Consider {0, 1} under the uniform measure. Let = 12 ... {0, 1} be random in the sense of Martin-Lof. (a) Show

[13] Consider {0, 1}∞ under the uniform measure. Let ω =

ω1ω2 ... ∈ {0, 1}∞ be random in the sense of Martin-L¨of.

(a) Show that ζ = ωnωn+1 ... is Martin-L¨of random for each n.

(b) Show that ζ = xω is Martin-L¨of random for each finite string x.

Comments. Source: [C. Calude and I. Chitescu, Bolletino U.M.I., (7)

3-B(1989), 229–240].