[Merged by Bors] - feat: Bergelson's Intersectivity Lemma #11143
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PR summary 65ce6d61aaImport changes for modified filesNo significant changes to the import graph Import changes for all files
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Cherry-picked from #11143 and renamed. Co-authored-by: @YaelDillies
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Cherry-picked from #11143 and moved to reuse `ENNReal.div_self_le_one`. Co-Authored-By: @YaelDillies
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| @@ -1128,7 +1128,7 @@ theorem lintegral_liminf_le {f : ℕ → α → ℝ≥0∞} (h_meas : ∀ n, Mea | |||
| lintegral_liminf_le' fun n => (h_meas n).aemeasurable | |||
| #align measure_theory.lintegral_liminf_le MeasureTheory.lintegral_liminf_le | |||
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| theorem limsup_lintegral_le {f : ℕ → α → ℝ≥0∞} {g : α → ℝ≥0∞} (hf_meas : ∀ n, Measurable (f n)) | |||
| theorem limsup_lintegral_le {f : ℕ → α → ℝ≥0∞} (g : α → ℝ≥0∞) (hf_meas : ∀ n, Measurable (f n)) | |||
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AFAIR, you've changed from explicit to implicit in some other cases. Does (g := _) work for you here?
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This is different from the other cases you are thinking about in that g appears neither on the LHS or RHS, so it can only be unified for if we already have proofs of hf_meas and h_bound, which is impractical (especially if f and g are big).
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Cherry-picked from #11143 and renamed. Co-authored-by: Yaël Dillies <[email protected]>
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Prove a weak version of the Bergelson intersectivity lemma. The proof gives the strong version, but we need natural density to state it. This is a prerequisite to Tao and Ziegler's recent paper [Infinite partial sumsets in the primes](https://arxiv.org/abs/2301.10303). spaces Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com> fix MeasureTheory.Integral.Lebesgue lint
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@urkud, I will merge this when I next access my computer (tonight or tomorrow) unless you object |
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Prove a weak version of the Bergelson intersectivity lemma. The proof gives the strong version, but we need natural density to state it. This is a prerequisite to Tao and Ziegler's recent paper [Infinite partial sumsets in the primes](https://arxiv.org/abs/2301.10303).
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Prove a weak version of the Bergelson intersectivity lemma. The proof gives the strong version, but we need natural density to state it. This is a prerequisite to Tao and Ziegler's recent paper Infinite partial sumsets in the primes.
preimage_subset_of_surjOn#14421a * a⁻¹#14423See leanprover-community/mathlib3#18732