Let be a -finite measure and let be a nonnegative -additive and finite function, both

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Let μ be a σ-finite measure and let φ be a nonnegative σ-additive and finite function, both defined on the measurable space ((, A). Then show that φ << μ is equivalent to the following: for every ( > 0, there exists ( = ( (() > 0 such that μ (A) < ( implies φ (A) < (.
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