The relation $P\ll\widetilde P$ is an instance of <absolute continuity of measures>: it means that every $\widetilde P$-null <event> is also $P$-null,
$$
\widetilde P(A)=0\implies P(A)=0.
$$
By the <Radon-Nikodym theorem>, this is equivalent to the existence of a nonnegative <Radon-Nikodym derivative> $dP/d\widetilde P$ whose $\widetilde P$-expectation is one.

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 202 / 5 / a / i / Solution

 Solution

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