11. (a) Lengths of successive coverings are 1, 2/3, 4/9, 8/27, ..., 2n/3n, ... . Since this last is (2/3)n, the Cantor MTS has length 0.
(b) Lengths removed = 1/3 + 2/9 + 4/27 + ... = (1/3)(1 + 2/3 + 4/9 + ...). In parentheses is a geometric series with ratio 2/3, so the series sums to 1/(1 - 2/3) = 3. Consequently, the lengths of the intervals removed sum to (1/3)3 = 1. Since we remove intervals from an interval of length 1, the Cantor MTS has remaining length 0.
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