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What are the assumptions to a measure to the Lebesgue Differentiation Theorem be True?

What is(if there is) a practical way to find the decomposition of a measure $\lambda$ in relation to a measure $\mu$?

OBS: I am only interested on non negative measure, but answers dealing with signed measures are welcomed as well.

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Radon-Nikodym theorem will be a nice reference. – Sangchul Lee Mar 7 '12 at 3:28

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