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Given (n_k), a strictly monotone increasing sequence of integers we consider the nonconventional ergodic/Birkhoff averages M_N^{\\alpha}f(x). The f-rotation set is Gamma_f={\\alpha \\in G: M_N^{\\alpha} f(x) converges for m a.e. x as N\\to \\infty .} We prove that if G is a compact locally connected Abelian group and f: G -> R is a measurable function then from m(Gamma_f)>0 it follows that f \\in L^1(G). 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