Basic Properties
Let (Ω, M, P) be a probability space, and let N be a σ-subalgebra of M.
- Conditioning with respect to N is linear on the space of integrable real random variables.
- More generally, for every integrable N–measurable random variable Y on Ω.
- for all B ∈ N and every integrable random variable X on Ω.
- Jensen's inequality holds: If ƒ is a convex function, then
- Conditioning is a contractive projection
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- for any s ≥ 1.
Read more about this topic: Conditional Expectation
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