  We consider an abstract space of measurable linear cocycles and we assume the
availability in this space of some appropriate uniform large deviation type
estimates. Under these hypotheses we establish the continuity of the Oseledets
filtration and decomposition as functions of the cocycle. The same assumptions
lead in [6] to a general continuity theorem for the Lyapunov exponents. This
result and other technical estimates derived in [6], along with the inductive
scheme based on the Avalanche Principle, are the main ingredients of the
arguments in this paper.
  We also give a new proof of the classical Multiplicative Ergodic Theorem of
V. Oseledets, using the Avalanche Principle (AP).
  This is a draft of a chapter in our forthcoming research monograph [6].
