= Quadratic covariation under an absolutely continuous measure change
For continuous <semimartingales> and $Q\ll P$, their <quadratic covariation> has the same version under the two <probability measures>, up to $Q$-<indistinguishability of stochastic processes>. The dyadic product sums have the same limit by <uniform convergence on compacts in probability under an absolutely continuous measure change>. Uniqueness of a limit in <probability> identifies that limit with the bracket under $Q$. <Semimartingale stability under an absolutely continuous measure change> supplies the correct class under $Q$: a <local martingale> need not remain a <local martingale>. Taking the two processes equal proves the same statement for <quadratic variation> without a separate assumption.
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