## Theorem

Let and be measures on with , a sub -algebra and an integrable random variable () then

## Proof

Thus

Hence

We note that

is -measurable (it is the result of a projection) and that

Hence

as required.

Let and be measures on with , a sub -algebra and an integrable random variable () then

Thus

Hence

We note that

is -measurable (it is the result of a projection) and that

Hence

as required.

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