Problem regarding the intervals or half-lines

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In the proof of Proposition 12.1.1, a 1-1 measurable function f from R onto [0, 1] was constructed by representing each space as a union of countably many disjoint intervals and letting f be monotone from each interval in R to an interval in [0, 1]. Show that this cannot be done with only finitely many intervals or half-lines.

Reference no: EM13990700

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