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Borel Measurable and Borel Functions

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1).Let f(X) : R -> R be the following:
f(x) = { 1 if x is in Q (rationals) , 0 if x is not in Q ( irrational)}
Prove that f(x) is Borel measurable ( Borel functions).

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Borel measurability and Borel functions are investigated. The solution is detailed and well presented.

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