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June 23rd, 2011, 11:11 PM   #1
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a question about Lebesgue measurable function

Please give a Lebesgue measurable subset E of Rn
and a Lebesgue measurable and finite-valued function f on E
satisfies
there doesn't exist a sequence of Lebesgue measurable subsets {Ek}k=1,2,...
of E
such that
(1)the untion of Ek is E;
(2)the restriction of f to every set Ek is continuous on Ek.
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