Independence and Product Measures
Let (Ω, F, P) be a probability space and let X : Ω → ℝ2 be a vector valued function, i.e., the values are vectors in ℝ2. For each w ∈ Ω, let X1(w) = (X1(w), X2(w)), where X 1 (w)) and X2(w) are the components of X(w) with respect to the canonical basis of ℝ2 consisting of el = (1, 0) and e2 = (0, 1).
KeywordsProbability Space Boolean Algebra Product Measure Borel Subset Borel Function
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