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Cantor Sets

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1. Show that the Cantor function c: [0, 1] → [0, 1] is continuous.

To do this, I know I need to use the fact that c is monotone, but I'm having difficulty from there.

2. Compute ∫c, where c is considered to be an element of L+(R). (let c(x) =0 for x not in [0, 1])

Here, c is the Cantor Function and L+(R) consists of functions which are almost everywhere the limit of a non-decreasing sequence of step functions for which the sequence (∫cn) is bounded.

3. Show that ¼ is in the Cantor set.

See attached file for full problem description.

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Cantor sets are investigated. The solution is detailed and well presented.

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