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[Merged by Bors] - refactor(MeasureTheory): redefine on measures #10714

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Commits on Feb 19, 2024

  1. refactor(MeasureTheory): redefine on measures

    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`
    urkud committed Feb 19, 2024
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