Let (1, (2 be two spaces and let A, Ai ( (1, B, Bi ( (2, i
Question:
(i) (A1 × B1) − (A2 × B2) = [(A1 ( A2] × (B1 - B2) + [(A1 - A2)] × B1].
(ii) A × B = (, if and if at least one of A, B is (.
(iii) If Ai × Bi, i = 1, 2 are ( (, then A1 × B2 ( A2 × B2, if and only if A1 ( A2, B1 ( B2.
(iv) If A1 × B1 = A2 × B2 ( (, then A1 = A2 and B1 = B2.
(v) Let A × B, Ai × Bi, i = 1, 2 be ( (. Then A × B = (A1 × B1) + (A2 × B2), if and only if A = A1 + A2 and B = B1 = B2, or A = A1 = A2 and B = B1 + B2.
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i Either by the inclusion process or as follows A 1 B 1 A 2 B 2 A 1 B 1 A 2 B 2 c A 1 B 1 A 2 B c 2 A c 2 2 by Lemma 2 A 1 B 1 A 2 B c 2 A 1 B 1 A c 2 2 A 1 A 2 B 1 B c 2 A 1 A c 2 B 1 2 clearly A 1 A ...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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