Then Y is \ sigma ( X )-measurable if and only if Y = g ( X ) for some Borel measurable function g : R ^ n \ rightarrow R ^ n.
2.
A new random variable " Y " can be defined by applying a real Borel measurable function g \ colon \ mathbb { R } \ rightarrow \ mathbb { R } to the outcomes of a real-valued random variable X.
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