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doc(MeasureTheory): tidy backticks (#31703)
Issues found and fixed with help from Codex.
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Mathlib/MeasureTheory/Group/Measure.lean

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@@ -876,7 +876,7 @@ instance _root_.ContinuousMulEquiv.isHaarMeasure_map [BorelSpace G] [IsTopologic
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[IsTopologicalGroup H] (e : G ≃ₜ* H) : (μ.map e).IsHaarMeasure :=
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e.toMulEquiv.isHaarMeasure_map μ e.continuous e.symm.continuous
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/-- A convenience wrapper for MeasureTheory.Measure.isAddHaarMeasure_map`. -/
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/-- A convenience wrapper for `MeasureTheory.Measure.isAddHaarMeasure_map`. -/
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instance _root_.ContinuousLinearEquiv.isAddHaarMeasure_map
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{E F R S : Type*} [Semiring R] [Semiring S]
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[AddCommGroup E] [Module R E] [AddCommGroup F] [Module S F]

Mathlib/MeasureTheory/Integral/CircleAverage.lean

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@@ -53,7 +53,7 @@ noncomputable def circleAverage : E :=
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lemma circleAverage_def :
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circleAverage f c R = (2 * π)⁻¹ • ∫ θ in 0..2 * π, f (circleMap c R θ) := rfl
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/-- Expression of `circleAverage´ in terms of interval averages. -/
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/-- Expression of `circleAverage` in terms of interval averages. -/
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lemma circleAverage_eq_intervalAverage :
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circleAverage f c R = ⨍ θ in 0..2 * π, f (circleMap c R θ) := by
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simp [circleAverage, interval_average_eq]
@@ -68,7 +68,7 @@ lemma circleAverage_eq_intervalAverage :
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one_smul]
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/--
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Expression of `circleAverage´ with arbitrary center in terms of `circleAverage` with center zero.
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Expression of `circleAverage` with arbitrary center in terms of `circleAverage` with center zero.
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-/
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lemma circleAverage_fun_add :
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circleAverage (fun z ↦ f (z + c)) 0 R = circleAverage f c R := by

Mathlib/MeasureTheory/Integral/IntervalAverage.lean

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@@ -32,7 +32,8 @@ open scoped Interval
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variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
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/-- `⨍ x in a..b, f x` is the average of `f` over the interval `Ι a w.r.t. the Lebesgue measure. -/
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/-- `⨍ x in a..b, f x` is the average of `f` over the interval `Ι a b` w.r.t. the Lebesgue
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measure. -/
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notation3 "⨍ "(...)" in "a".."b",
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"r:60:(scoped f => average (Measure.restrict volume (uIoc a b)) f) => r
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