  In 1968, V.I. Oseledets formulated the question of convergence in the
Birkhoff theorem and the multiplicative ergodic theorem for measurable cocycles
over flows under the condition of integrability for each individual t. A.M.
Stepin and the author established (2016) the convergence along subsets of time
of density 1. In this note, we show that moreover the convergence is fulfilled
modulo time subsets of finite measure.
