2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107516Let ${\bf X}=(X, Σ, m, τ)$ be a dynamical system. We prove that the bilinear series $\sideset{}{'}\sum_{n=-N}^{N}\frac{f(τ^nx)g(τ^{-n}x)}{n}$ converges almost everywhere for each $f,g\in L^{\infty}(X).$ We also give a proof along the same lines of Bourgain's analog result for averages.28 pages, no figuresClassical Analysis and ODEsDynamical Systems42B20; 42B25; 37A05text