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refactor(MeasureTheory): golf Mathlib/MeasureTheory/Function/ConditionalExpectation/AEMeasurable (leanprover-community#38876)
- rewrites `memLp_trim_of_mem_lpMeasSubgroup` to use `hf.mk f` instead of unpacking `hf.choose` - shortens the norm comparison to a direct rewrite with `eLpNorm_trim` and `hf.ae_eq_mk` Extracted from leanprover-community#38104 [![Open in Gitpod](https://gitpod.io/button/open-in-gitpod.svg)](https://gitpod.io/from-referrer/)
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Mathlib/MeasureTheory/Function/ConditionalExpectation/AEMeasurable.lean

Lines changed: 3 additions & 8 deletions
Original file line numberDiff line numberDiff line change
@@ -134,14 +134,9 @@ theorem memLp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : Lp F p μ)
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MemLp (mem_lpMeasSubgroup_iff_aestronglyMeasurable.mp hf_meas).choose p (μ.trim hm) := by
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have hf : AEStronglyMeasurable[m] f μ :=
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mem_lpMeasSubgroup_iff_aestronglyMeasurable.mp hf_meas
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let g := hf.choose
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obtain ⟨hg, hfg⟩ := hf.choose_spec
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change MemLp g p (μ.trim hm)
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refine ⟨hg.aestronglyMeasurable, ?_⟩
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have h_eLpNorm_fg : eLpNorm g p (μ.trim hm) = eLpNorm f p μ := by
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rw [eLpNorm_trim hm hg]
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exact eLpNorm_congr_ae hfg.symm
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rw [h_eLpNorm_fg]
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change MemLp (hf.mk f) p (μ.trim hm)
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refine ⟨hf.stronglyMeasurable_mk.aestronglyMeasurable, ?_⟩
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rw [eLpNorm_trim hm hf.stronglyMeasurable_mk, eLpNorm_congr_ae hf.ae_eq_mk.symm]
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exact Lp.eLpNorm_lt_top f
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/-- If `f` belongs to `Lp` for the measure `μ.trim hm`, then it belongs to the subgroup

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