Hi everyone
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
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
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 .