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Mathlib/Dynamics/BirkhoffSum/Maximal.lean

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@@ -215,9 +215,7 @@ theorem birkhoffAverageSupSet_eq_birkhoffSupSet {f : α → α} {g a} (ha : 0 <
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rw [birkhoffSum_zero] at h
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exact lt_irrefl 0 h
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· exact birkhoffAverage_iff_birkhoffSum (by positivity)
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conv =>
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enter [1, 1, x, 1, n]
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rw [this]
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simp_rw [this]
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section MeasurePreserving
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@@ -278,7 +276,7 @@ variable {E : Type*} [NormedAddCommGroup E] {g : α → E} (hg : Integrable g μ
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include hg
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/-- Maximal ergodic theorem: maximal ergodic operator satisfies a weak-type inequality. -/
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/-- Maximal ergodic theorem: the maximal ergodic operator satisfies a weak-type inequality. -/
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public theorem meas_birkhoffAverageSupSet_smul_const_le_norm :
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⨆ a, a * μ.real (birkhoffAverageSupSet f (fun x ↦ ‖g x‖) a) ≤ ∫ x, ‖g x‖ ∂μ := by
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refine ciSup_le fun a ↦ ?_

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