= Cameron-Martin quasi-invariance of enhanced Brownian motion
{c}
For a deterministic path $h$ in the <Cameron-Martin space of Wiener measure>, the law of $T_h\mathbf B$ is equivalent to the law of <enhanced Brownian motion>. The <Cameron-Martin theorem> gives equivalence for the underlying Brownian paths; the canonical enhancement of the translated path is exactly the rough-path translation, including its mixed area terms. Continuity of this translation transfers small-ball positivity at the identity to every control signature.
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