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Multiple return times theorems for weakly mixing systems. (English) Zbl 0985.37004
The author proves the pointwise convergence of the expression \[ {1\over N}\sum^N_{n=0} a_n g(R^n z) \] where \((Z,K,\nu,R)\) is an ergodic dynamical system on a probability measure space \((Z,K,\nu)\), the sequence of scalars \(a_n\) has the form \[ a_n= a_n(x, y_1,y_2,\dots, y_J)= \Biggl(\prod^H_{i= 1} f_i(T^{b,n}x)\Biggr) \Biggl(\prod^J_{j=1} g_j(S^n_j y_j)\Biggr), \] \((b_1,b_2,\dots, b_H)\in Z^H\), \(J\) is a positive integer, the functions \(f_i\) and \(g_j\) are bounded and \((X,F,\mu, T)\) and \((Y,G_j, m_j, S_j)\) are weakly mixing systems.

MSC:
37A25 Ergodicity, mixing, rates of mixing
93E25 Computational methods in stochastic control (MSC2010)
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