Let f be an inner function with f(0)=0 which is not a rotation and let fn its n-th iterate. {an} sequence of complex numbers. We prove that the series ∑anfn(ξ) converges at almost every point ξ unit circle if only ∑|an|2<∞. The main step in proof to show under this assumption, F=∑anfn has bounded mean oscillation. also F on disc ∑|an|<∞. Finally we describe sequences coefficients such belongs o...