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Let (Ω,F,μ) be a probability space and let T="P1P2⋯Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1,F2,…,Fd.
Let (E,F,μ) be a probability space, and let P be a Markov operator on L2 with 1 a simple eigenvalue such that μP="μ (i.e. μ is an invariant probability measure of P).
Let be a probability space.
(H3): Let (( X,mathcal{B},mu ) ) be a probability space.
Let Open image in new window be a probability space.
Let (P, Ω, A) be a probability space.
Similar(6)
Then, is a probability space.
If and is -integrable, where is a probability space, then.
We suppose that ( Ω, F, P ) is a probability space.
Then ((Omega, P, {mathcal{F}_{t}})) is a probability space.
Note that ((mathbb {R}^n,gamma )) is a probability space, since (gamma (mathbb {R}^n)=1).
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