All sets figuring below are subsets of the product space W 1 ´ W 2 . Then
Question:
(i) E Ã F implies Ew1 Ã Ew1 and Ew2 Ã Ew2, w1 ÃŽ W1, w2 ÃŽ, W2.
(ii) E Ç F Ø implies Ew1 ÇEw1 = Ew2 Ç Ew2 = Ø, w1 Î W1, w2 Î W2.
(iii) For n = 1, 2,€¦.
And in particular,
w2 ÃŽ W2.
(iv) For n = 1, 2,€¦.,
w2 ÃŽ W2.
(v) (Ec) w1 = (Ew1)c, (Ec) w2 = (Ew2)c, w1 ÃŽ W1, w2 ÃŽ W2.
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i 2 E 1 implies that 1 2 E so that 1 2 F and then 2 F 1 Thus E 1 F 1 Similarly E 2 F 2 ii If E 1 F 1 ...View the full answer
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Related Book For 
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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