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Let (X,M) be a measurable space, let µ, ν be two finite measures on this space,...

Let (X,M) be a measurable space, let µ, ν be two finite measures on this space, and let E ∈ M be such that µ(E) > ν(E).

Then show that there exists P ∈ M with P ⊆ E such that µ(P) > ν(P) and µ(F) ≥ ν(F) for every F ∈ M with F ⊆ P.

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