Consider the measure space (W, A, ), and define the classes A* and A as follow: A*
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Consider the measure space (W, A, μ), and define the classes A* and A̅ as follow:
A* = {A D M: A Î A, M Í N with N Î A and μ(N) = 0},
A̅ = {A È M: A Î A, M Í N with N Î A and μ(N) = 0}.
Then show that
(i) A D M = (A – N) È [N Ç (A D M)].
(ii) A È M = (A – N) D [N Ç (A È M)].
From parts (i) and (ii), conclude that
(iii) A* = A̅
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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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