Clark Butler University of Chicago I will outline a proof that any measurable solution to the cohomological equation for Holder linear cocycles over a uniformly hyperbolic system coincides almost everywhere with a Holder solution. I will focus on establishing uniform growth estimates for the cocycle from the existence of a measurable solution. This will be done by proving, more generally, that any Holder linear cocycle over a uniformly hyperbolic system which preserves a measurable inner product must also preserve a continuous inner product.