Convergence of spherical averages for actions of free groups
نویسندگان
چکیده
Let (X, ν) be a probability space and suppose a free group Fm withm generators acts on (X, ν) by measure-preserving transformations. Let {a1, . . . , am} be a set of free generators for Fm and let T1, . . . , Tm : X → X be transformations corresponding to the generators. Write T−i = T −1 i for i = 1, . . . ,m, and set A = {−m, . . . ,−1, 1, . . . ,m}. We also have the action Fm on L1(X, ν), defined by Tgφ = φ ◦ Tg−1 , g ∈ Fm. Consider the set WA of all finite words over the alphabet A: WA = {w = w1w2 . . . wn| wi ∈ A}.
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