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refactor(MeasureTheory/Integral/DominatedConvergence): golf IntegrableOn.continuousOn_primitive_Ici and ..._Iic
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Mathlib/MeasureTheory/Integral/DominatedConvergence.lean

Lines changed: 2 additions & 8 deletions
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@@ -792,10 +792,7 @@ section PrimitiveIci
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theorem IntegrableOn.continuousOn_primitive_Ici [NoAtoms μ] {a : ℝ}
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(hf : IntegrableOn f (Ici a) μ) :
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ContinuousOn (fun b ↦ ∫ x in Ici b, f x ∂μ) (Ici a) := by
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conv =>
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arg 1
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ext b
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rw [integral_Ici_eq_integral_Ioi]
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simp_rw [integral_Ici_eq_integral_Ioi]
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exact (hf.mono_set Ioi_subset_Ici_self).continuousOn_primitive_Ioi
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end PrimitiveIci
@@ -805,10 +802,7 @@ section PrimitiveIci
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theorem IntegrableOn.continuousOn_primitive_Iic [NoAtoms μ] {a : ℝ}
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(hf : IntegrableOn f (Iic a) μ) :
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ContinuousOn (fun b ↦ ∫ x in Iic b, f x ∂μ) (Iic a) := by
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conv =>
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arg 1
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ext b
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rw [integral_Iic_eq_integral_Iio]
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simp_rw [integral_Iic_eq_integral_Iio]
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exact (hf.mono_set Iio_subset_Iic_self).continuousOn_primitive_Iio
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end PrimitiveIci

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