  We provide an explicit uniform bound on the local stability of ergodic
averages in uniformly convex Banach spaces. Our result can also be viewed as a
finitary version in the sense of T. Tao of the Mean Ergodic Theorem for such
spaces and so generalizes similar results obtained for Hilbert spaces by
Avigad, Gerhardy and Towsner (arXiv:0706.1512v2 [math.DS]) and T. Tao
(arXiv:0707.1117v1 [math.DS]).
