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The Lebesgue measure is not defined for all subsets of R. It is defined on the Lebesgue sigma algebra which is larger than the Borel sigma algebra. You could i
by vostok 9y ago
The Lebesgue measure is not defined for all subsets of R. It is defined on the Lebesgue sigma algebra which is larger than the Borel sigma algebra.
You could instead choose a sigma algebra that does not contain {0}. Trivially, you could choose the standard Lebesgue measure restricted to {{}, R}.
- RBerenguel 9y agoOh well, I was thinking of a measure where 0 was in some Borel set of it, otherwise it loses a bit the fun of it
- vostok 9y agoIn this case, 0 is contained in R which is a Borel set and is part of the sigma algebra on which the measure is defined.
- RBerenguel 9y agoI mean, one with a more rich sigma algebra.