We calculate a certain mean-value of meromorphic functions by using specific ergodic transformations, which we call affine Boolean transformations. We use Birkhoff's ergodic theorem to transform the mean-value into a computable integral which allows us to completely determine the mean-value of this ergodic type. As examples, we introduce some applications to zeta functions and L-functions. We also prove an equivalence of the Lindelöf hypothesis of the Riemann zeta function in terms of its certain ergodic value distribution associated with affine Boolean transformations.
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