Theorem 9.10 allows us to avoid some calculations in the last paragraph of the proof of Theorem 13.3. Suppose X is a continuous semimartingale under P and Q is a probability measure equivalent to P....

Theorem 9.10 allows us to avoid some calculations in the last paragraph of the proof of Theorem 13.3. Suppose X is a continuous semimartingale under P and Q is a probability measure equivalent to P. That is, a set is a null set for P if and only if it is a null set for Q. Show X is a semimartingale under Q and the quadratic variation of X under P equals the quadratic variation of X under Q.