Commit 2024-08-15 14:22 665c7ae3
View on Github →feat(MeasureTheory): method of exhaustion (#14471)
If μ, ν
are two measures with ν
s-finite, then there exists a set s
such that μ
is sigma-finite on s
, and for all sets t ⊆ sᶜ
, either ν t = 0
or μ t = ∞
. The technique used to obtain this result is what Halmos calls the "method of exhaustion".
We use this to prove that if μ ≪ ν
and ν
is s-finite, then μ
is s-finite.
This PR also moves the definition of sigmaFiniteSet
to the new file and refactors it with the new definition sigmaFiniteSetWRT
.