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