[Merged by Bors] - feat(outer_measure): define bounded_by #5314
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bounded_by is a more general version of of_function, which has been used in the library already also add some complete lattice lemmas
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| satisfying `μ s ≤ m s` for all `s : set α`. This is the same as `outer_measure.of_function`, | ||
| except that it doesn't require `m ∅ = 0`. -/ | ||
| def bounded_by : outer_measure α := | ||
| outer_measure.of_function (λ s, ⨆ (h : s.nonempty), m s) (by simp [empty_not_nonempty]) |
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Is ⨆ (h : s.nonempty), m s more convenient than if s.nonempty then m s else 0 or function.update m ∅ 0?
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I think the answer is "no". I'm just using what was used before in the measure theory library.
I think ⨆ (h : s.nonempty), _ is better if you don't use classical logic (since it doesn't require any decidability), but we moved away from that anyway. I'm happy to change it to function.update at some point.
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`bounded_by` wrapper around `of_function` that drops the condition that `m ∅ = 0`. Refactor `Inf_gen` to use `bounded_by`. I am also planning to use `bounded_by` for finitary products of measures. Also add some complete lattice lemmas
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bounded_bywrapper aroundof_functionthat drops the condition thatm ∅ = 0.Refactor
Inf_gento usebounded_by.I am also planning to use
bounded_byfor finitary products of measures.Also add some complete lattice lemmas