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Daniele Tampieri
Daniele Tampieri
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The two definitions alluded to in the title can be found here: http://en.wikipedia.org/wiki/Separable_sigma_algebrain the relevant Wikipedia entry (one is that the $\sigma$-algebra is countably generated, the other is pretty much the standard usage of the word separable wrt the semi-metric given by the measure). Why are they equivalent?

The two definitions alluded to in the title can be found here: http://en.wikipedia.org/wiki/Separable_sigma_algebra (one is that the $\sigma$-algebra is countably generated, the other is pretty much the standard usage of the word separable wrt the semi-metric given by the measure). Why are they equivalent?

The two definitions alluded to in the title can be found in the relevant Wikipedia entry (one is that the $\sigma$-algebra is countably generated, the other is pretty much the standard usage of the word separable wrt the semi-metric given by the measure). Why are they equivalent?

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Kestutis Cesnavicius
Kestutis Cesnavicius
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Separable sigma-algebra: equivalence of two definitions

The two definitions alluded to in the title can be found here: http://en.wikipedia.org/wiki/Separable_sigma_algebra (one is that the $\sigma$-algebra is countably generated, the other is pretty much the standard usage of the word separable wrt the semi-metric given by the measure). Why are they equivalent?