I cannot find the solution to this problem,
Let A a Lebesgue Measurable Set; Prove that given then exists Lebesgue Measurable such that m(B) = b
I appreciate your help
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Originally Posted by everk Let A a Lebesgue Measurable Set; Prove that given then exists Lebesgue Measurable such that m(B) = b Let denote the characteristic function of (so that if , and if ). For each real number , let Show that is continuous and use the intermediate value theorem to deduce that there exists such that
Does that work if ?
Originally Posted by Bruno J. Does that work if ? It will certainly need a bit of adjustment if . I think that you would then have to start by looking at , which can be made arbitrarily large if is small enough and is large enough. Then reduce until the integral reaches the value .
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