Rational translates of Fat Cantor set as positive but not full measure for each interval
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I was wondering how whether this works: Choose $A=cup_r in Qr+F$ where F denotes the Fat Cantor Set.
To be precise, if ü denotes Lebesgue measure, how would one show that this A as a Borel set AâÂÂR such that
$0<ü(Aâ©I)<ü(I)$
for every interval I in R?
A is not R by Baire Category theorem. But I haven't made much progress thereafter.
real-analysis measure-theory
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up vote
0
down vote
favorite
I was wondering how whether this works: Choose $A=cup_r in Qr+F$ where F denotes the Fat Cantor Set.
To be precise, if ü denotes Lebesgue measure, how would one show that this A as a Borel set AâÂÂR such that
$0<ü(Aâ©I)<ü(I)$
for every interval I in R?
A is not R by Baire Category theorem. But I haven't made much progress thereafter.
real-analysis measure-theory
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I was wondering how whether this works: Choose $A=cup_r in Qr+F$ where F denotes the Fat Cantor Set.
To be precise, if ü denotes Lebesgue measure, how would one show that this A as a Borel set AâÂÂR such that
$0<ü(Aâ©I)<ü(I)$
for every interval I in R?
A is not R by Baire Category theorem. But I haven't made much progress thereafter.
real-analysis measure-theory
I was wondering how whether this works: Choose $A=cup_r in Qr+F$ where F denotes the Fat Cantor Set.
To be precise, if ü denotes Lebesgue measure, how would one show that this A as a Borel set AâÂÂR such that
$0<ü(Aâ©I)<ü(I)$
for every interval I in R?
A is not R by Baire Category theorem. But I haven't made much progress thereafter.
real-analysis measure-theory
real-analysis measure-theory
asked Sep 4 at 9:15
Ronit Debnath
531115
531115
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