I'm now studying Lebesgues measure on R^n, and when we finished constructing L (all measurable sets), we moved on to Borel sets and so on.(adsbygoogle = window.adsbygoogle || []).push({});

My question is, is there is no way of extending the Lebesgues measure on a larger family than L? Can it be done while still saving the nice properties of the Lebesgues measure (invariance under isometries, at the least)?

If so, how, and if not, why (as in proof)?

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# Lebesgues's Sigma Algebra

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