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Lower Measures

True or False problem.

m_* (A) = Sup sum_i | M_i| ( U M_i is subset of A)

Where m_* is the inner measure
M_i doesn't equal M_j for i doesn't equal j ( i.e, they are disjoint)

Prove it or show a counterexample and explain it to show how the equality doesn't hold.

Solution Summary

Lower measures are investigated. The solution is detailed and well presented.