Abstract: In 2017, Baraviera and Duarte extended a classical theorem from Le Page. They obtained an elegant proof for the local Holder continuity of the Lyapunov exponents of random linear cocycles defined over the Bernoulli Shift under generic hypothesis. The authors proved local Holder continuity with respect to the cocycle, with a fixed measure. The main tools are Furstenberg`s Formula and regularity properties from the stationary measure. In the same context, with analogous hypothesis, we will show that, for a fixed cocycle, the top Lyapunov exponent is locally Holder continuous with respect to the measure, in Wasserstein`s metric. In particular, this implies the result from Baraviera and Duarte. This is a joint work with Silvius Klein.