=+34.13. Let Z2 be the Hilbert space of square-integrable random variables on (2, 9, P). For &

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=+34.13. Let Z2 be the Hilbert space of square-integrable random variables on

(2, 9, P). For & a o-field in F, let Me be the subspace of elements of L2 that are measurable . Show that the operator P , defined for X EL2 by PX = E[X]]] is the perpendicular projection on M.

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