Let ${\bf X}=(X, \Sigma, m, \tau)$ be a dynamical system. We prove that thebilinear series $\sideset{}{'}\sum_{n=-N}^{N}\frac{f(\tau^nx)g(\tau^{-n}x)}{n}$converges almost everywhere for each $f,g\in L^{\infty}(X).$ We also give aproof along the same lines of Bourgain's analog result for averages.
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