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Unformatted text preview: ) be a measure space with ( X ) < , and let f be as in the previous problem. Give a direct proof, based on the denition of R f d on p.50, of the following fact: > , > 0 such that from E M and ( E ) < it follows Z E f d < . Remark. This fact is known as the absolute continuity of the Lebesgue integral, and it is contained in Corollary 3.6 on p.89. #5. Let ( X, M , ) be a measure space with ( X ) < . Show that d ( f + g ) d ( f ) + d ( g ) for all measurable functions f, g on X, where d ( f ) := inf > + { x X :  f ( x )  } ....
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 Fall '08
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