The Cantor ternary set C is defined to be the set of all real n... | Filo
The Cantor ternary set C is defined to be the set of all real n... | Filo
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4. (a) Prove that the Cantor set has measure zero. Don't forget to explain why it is measurable. (b) Give an example of a set in [0, 1] that has measure 1, but does not contain any open intervals. Justify your answer.
4. (a) Prove that the Cantor set has measure zero. Don't forget to expl…
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The Cantor set, named after the German mathematician George Cantor (1845 - 1918), is constructed as follows. We start with the closed interval [0, 1] and remove the open interval ( (1)/(3), (2)/(3) ). That leaves the two intervals [ 0, (1)/(3) ] and [ (2)/(3), 1 ] and we remove the open middle third of each. Four intervals remain and given we remove the open middle third of each of them. We continue this procedure indefinitely, at each step removing the open middle third of every interval that r
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