Question: Could you please solve this problem? Q2. Recall that we proved Lebesgue's Theorem that every measure on 0, 1 can be written as the sum

Could you please solve this problem?

Q2. Recall that we proved Lebesgue's Theorem that every measure on 0, 1 can be written as the sum of two measures, one absolutely continuous w.r.t. Lebesgue measure and one disjoint from Lebesgue measure. A measure / defined on the Borel o-algebra B of R is called a reg- ular Borel measure if (i) #(F)

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