Cameron-Martin theorem

Translation of Wiener measure by a path $h$ is equivalent to Wiener measure exactly when $h$ belongs to the Cameron-Martin space of Wiener measure. In that case the density isTranslation by any continuous path outside that space produces a singular measure.

For the Cameron-Martin space of Wiener measure path $h(s)=\mu s$, the Cameron-Martin theorem says that translation of Brownian motion by this linear function changes its law through time $t$ by the density