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.Let (X,M, ) be a finite measure space. Suppose X admits a sequence of finite partitions Fn consisting of measurable sets, such that sup{(F) :
.Let (X,M, ) be a finite measure space. Suppose X admits a sequence of finite partitions Fn consisting of measurable sets, such that sup{(F) : F Fn} 0 as n . Prove that for any t [0, (X)], there exists A M such that (A) = t. (We say (X,M, ) has the intermediate value property.)
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