Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 37 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 7 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 16 / 4 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 16 / 4 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 34 / 2 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 39 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 10 / 5 / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 32 / 6 / b / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 32 / 6 / b / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 7 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 33 / 5 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 33 / 5 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2007 / iii / Paper 33 / 6 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 30 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 30 / 3 / Solution

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Lebesgue measure is the unique translation-invariant $\sigma$-finite Borel measure on $\mathbb R$ normalized by $\lambda((0,1])=1$. Translation invariance follows by comparing translated measure with $\lambda$ on half-open intervals and applying uniqueness.


Lebesgue measure

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 Incoming links: Lebesgue measure