I'm having trouble, please can somebody help me? Prove that for all ε>0 there exists a closed set Fc[0,1] such that F = and λ(F)>1-ε, where λ is the Lebesgue measure. Thank you very much!
Follow Math Help Forum on Facebook and Google+
That sounds like a very difficult problem, if not impossible. The irrationals in the interval [0,1] are not closed, and I'm not sure I see how any subset of them can be closed. Are you sure this problem is solvable?
I have seen this problem as an exercise in two books, then I think there is a solution.
Originally Posted by eltondelamancha I'm having trouble, please can somebody help me? Prove that for all ε>0 there exists a closed set Fc[0,1] such that F = and λ(F)>1-ε, where λ is the Lebesgue measure. Thank you very much! This is an immediate consequence of the following lemma: A set has measure if and only if for all there exists an open set with The proof of this is easy: There exists a lower semicontinous function with then take
Nice thinking 'Jose27'
View Tag Cloud