= Finite-variation terms do not change quadratic variation
{title2=$[M+A]=[M]\quad(A\text{ continuous of finite variation})$}
On a compact interval, squared increments of a continuous <finite variation> process are bounded by its modulus of continuity at the mesh size times its total variation, and therefore vanish. The <Cauchy-Schwarz inequality> bounds the mixed increment sum by the square root of the product of the two squared-increment sums. The local-<martingale> sum is bounded in probability, so the mixed term also vanishes.
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