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The semi-invertible version of Oseledets' multiplicative ergodic theoremproviding a decomposition of the underlying state space of a random lineardynamical system into fast and slow spaces is deduced for a strongly measurablecocycle on a separable Banach space. This work represents a significantlysimplified means of obtaining the result, using measurable growth estimates onsubspaces for linear operators combined with a modified version of Kingman'ssubadditive ergodic theorem.

Constructing the Oseledets decomposition with subspace growth estimates