[Merged by Bors] - refactor(MeasureTheory): redefine ≤ on measures#10714
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[Merged by Bors] - refactor(MeasureTheory): redefine ≤ on measures#10714
≤ on measures#10714Conversation
Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. The reasons are: - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
fpvandoorn
reviewed
Feb 21, 2024
| #align ennreal.to_real_le_to_real ENNReal.toReal_le_toReal | ||
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| @[gcongr] | ||
| theorem toReal_mono (hb : b ≠ ∞) (h : a ≤ b) : a.toReal ≤ b.toReal := |
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unrelated to this PR: we should move finiteness to mathlib and add it as a gcongr discharger.
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Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. ### Reasons - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". ### Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
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Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. ### Reasons - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". ### Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
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≤ on measures≤ on measures
thorimur
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Feb 24, 2024
Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. ### Reasons - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". ### Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
thorimur
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Feb 26, 2024
Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. ### Reasons - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". ### Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
riccardobrasca
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Mar 1, 2024
Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. ### Reasons - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". ### Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
dagurtomas
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Mar 22, 2024
Redefine `≤` on `MeasureTheory.Measure` so that `μ ≤ ν ↔ ∀ s, μ s ≤ ν s` by definition instead of `∀ s, MeasurableSet s → μ s ≤ ν s`. ### Reasons - this way it is defeq to `≤` on outer measures; - if we decide to introduce an order on all `DFunLike` types **and** migrate measures to `FunLike`, then this is unavoidable; - the reasoning for the old definition was "it's slightly easier to prove `μ ≤ ν` this way"; the counter-argument is "it's slightly harder to apply `μ ≤ ν` this way". ### Other changes - golf some proofs broken by this change; - add `@[gcongr]` tags to some `ENNReal` lemmas; - fix the name `ENNReal.coe_lt_coe_of_le` -> `ENNReal.ENNReal.coe_lt_coe_of_lt`; - drop an unneeded `MeasurableSet` assumption in `set_lintegral_pdf_le_map`
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Redefine
≤onMeasureTheory.Measureso that
μ ≤ ν ↔ ∀ s, μ s ≤ ν sby definitioninstead of
∀ s, MeasurableSet s → μ s ≤ ν s.Reasons
≤on outer measures;DFunLiketypesand migrate measures to
FunLike, then this is unavoidable;"it's slightly easier to prove
μ ≤ νthis way";the counter-argument is
"it's slightly harder to apply
μ ≤ νthis way".Other changes
@[gcongr]tags to someENNReallemmas;ENNReal.coe_lt_coe_of_le->ENNReal.ENNReal.coe_lt_coe_of_lt;MeasurableSetassumptionin
set_lintegral_pdf_le_map