My masters thesis advisor was Martín Sambarino. I studied generalizations of Oseledets' ergodic theorem due to Kaimanovich, Karlsson, Margulis, and Ledrappier. Also, I give a self-contained proof of Oseledets' theorem (both the flag and splitting version) along those lines (showing that a certain sequence of positive definite symmetric matrices is close to a geodesic in the space of such matrices).