Prove komlos_convergence_L2 - #442
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RemyDegenne
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May 21, 2026
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| lemma komlos_convergence_L2 | ||
| (f : ℕ → Ω → E) {P : Measure Ω} : | ||
| (f : ℕ → Ω → E) {P : Measure Ω} [IsProbabilityMeasure P] (hf : UniformIntegrable f 1 P) : |
Owner
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Why do you need hf : UniformIntegrable f 1 P?
I see it used explicitly only in one place as hf.aestronglyMeasurable (I just looked at the github diff, I did not interact with the code yet). If that's the only use, you should replace hf with hf : AEStronglyMeasurable f P.
TBUGTB
reviewed
May 21, 2026
| grw [ih] | ||
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| omit [InnerProductSpace ℝ E] [CompleteSpace E] in | ||
| lemma memlp_indicator (f : Ω → E) {P : Measure Ω} [IsFiniteMeasure P] |
Contributor
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I think the name should be memLp_indicator. I also think it should be possible to generalise 2 to p.
TBUGTB
reviewed
May 21, 2026
| ∃ glim : E, Tendsto (fun n ↦ (η n).sum (fun m ηm ↦ ηm • x i m)) atTop (𝓝 glim) := by sorry | ||
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| lemma MeasureTheory.Lp.coeFn_finset_sum {α : Type*} {E : Type*} {m : MeasurableSpace α} |
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Can you move this and the next lemma to an appropriate file in the Auxiliary folder? They don't have anything directly to do with the Komlos lemma.
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