Question: Consider the measure space (W, A, ), and define the classes A* and A as follow: A* = {A D M: A A, M

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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