Unformatted text preview: → [0 , 1] be the Cantor-Lebesgue function (see SS Ch.1, Exercise 2) and let g : [0 , 1] → [0 , 2] be the function g ( x ) = x + f ( x ). Prove that g is a homeomorphism and m ( g ( C )) = 1, where C is the Cantor set. Then show that if B is a Lebesgue nonmeasurable subset of g ( C ) (see SS Ch.1, Exercise 32(b)), then g-1 ( B ) is not Borel but is Lebesgue measurable. 1...
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- Spring '10
- Math, measure, Lebesgue measure, SS Ch.1