  We prove a central limit theorem for the real and imaginary part and the
absolute value of the Riemann zeta-function sampled along a vertical line in
the critical strip with respect to an ergodic transformation similar to the
Boolean transformation. This result complements a result by Steuding who has
proven a strong law of large numbers for the same system. As a side result we
state a general central limit theorem for a class of unbounded observables on
the real line over the same ergodic transformation. The proof is based on the
transfer operator method.
