[Merged by Bors] - feat(measure_theory/measure/measure_space): better definition of to_measurable #11529
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sgouezel
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| @@ -360,6 +360,23 @@ lemma ae_le_set : s ≤ᵐ[μ] t ↔ μ (s \ t) = 0 := | |||
| calc s ≤ᵐ[μ] t ↔ ∀ᵐ x ∂μ, x ∈ s → x ∈ t : iff.rfl | |||
| ... ↔ μ (s \ t) = 0 : by simp [ae_iff]; refl | |||
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| lemma ae_le_set_inter {s' t' : set α} (h : s ≤ᵐ[μ] t) (h' : s' ≤ᵐ[μ] t') : | |||
| (s ∩ s' : set α) ≤ᵐ[μ] (t ∩ t' : set α) := | |||
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This is true for any filter, so it's available as h.inter h'. Same for ae_eq_inter.
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Thanks a lot. I have kept the lemmas for ease of discoverability, but I can remove them if you prefer.
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I think that I can golf the longest proof once #11547 is merged but let's merge this one first. |
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…easurable (#11529) Currently, `to_measurable μ t` picks a measurable superset of `t` with the same measure. When the measure of `t` is infinite, it is most often useless. This PR adjusts the definition so that, in the case of sigma-finite spaces, `to_measurable μ t` has good properties even when `t` has infinite measure.
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Pull request successfully merged into master. Build succeeded: |
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Currently,
to_measurable μ tpicks a measurable superset oftwith the same measure. When the measure oftis infinite, it is most often useless. This PR adjusts the definition so that, in the case of sigma-finite spaces,to_measurable μ thas good properties even whenthas infinite measure.