Question: Let X be a set, and define : 2^x [0,] by (E) = 0 if E is countable if E is uncountable (a) Prove that

Let X be a set, and define : 2^x [0,] by

(E) = 0 if E is countable

if E is uncountable

(a) Prove that is a measure on (X, 2^x).

(b) Let f : 2^x [0,] such that f is strictly positive on an uncountable subset of X. Prove that

integral of fx fd = .

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