Independence and Product Measures

J. C. Taylor
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J. C. Taylor: McGill University, Department of Mathematics and Statistics

Chapter Chapter III in An Introduction to Measure and Probability, 1997, pp 86-136 from Springer

Abstract: Abstract 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).

Keywords: Probability Space; Boolean Algebra; Product Measure; Borel Subset; Borel Function (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1007/978-1-4612-0659-0_3

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