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[Merged by Bors] - feat: integral of f x • g y over α × β #7627

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[Merged by Bors] - feat: integral of f x • g y over α × β #7627

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@urkud urkud commented Oct 11, 2023 •
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  • Generalize integral_prod_mul to integral_prod_smul, add Integrable.prod_smul.
  • Rename integrable_prod_mul to Integrable.prod_mul.
  • Add integral_fun_fst and integral_fun_snd.

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@urkud urkud added blocked-by-other-PR This PR depends on another PR which is still in the queue. awaiting-review The author would like community review of the PR t-measure-probability Measure theory / Probability theory labels Oct 11, 2023
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the blocked-by-other-PR This PR depends on another PR which is still in the queue. label Oct 11, 2023
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RemyDegenne approved these changes Oct 12, 2023
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Thanks!
bors d+

Mathlib/MeasureTheory/Constructions/Prod/Integral.lean
theorem integral_prod_mul {L : Type*} [IsROrC L] (f : α → L) (g : β → L) :
∫ z, f z.1 * g z.2 ∂μ.prod ν = (∫ x, f x ∂μ) * ∫ y, g y ∂ν := by
by_cases h : Integrable (fun z : α × β => f z.1 * g z.2) (μ.prod ν)
theorem integral_prod_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] (f : α → 𝕜) (g : β → E) :
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In Integrable.prod_smul, you generalized IsROrC to NontriviallyNormedField. Here you kept IsROrC. Is the generalization impossible here?

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To avoid integrability assumption, you need 𝕜 to be a complete space. Also, we need [NormedSpace Real 𝕜]. AFAICT, only IsROrC satisfy this.

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✌️ urkud can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added delegated and removed awaiting-review The author would like community review of the PR labels Oct 12, 2023
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urkud commented Oct 12, 2023

bors merge

@github-actions github-actions bot added the ready-to-merge This PR has been sent to bors. label Oct 12, 2023
bors bot pushed a commit that referenced this pull request Oct 12, 2023
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feat: integral of f x • g y over α × β (#7627)
bdd2abe 
* Generalize `integral_prod_mul` to `integral_prod_smul`, add `Integrable.prod_smul`.
* Rename `integrable_prod_mul` to `Integrable.prod_mul`.
* Add `integral_fun_fst` and `integral_fun_snd`.
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@bors bors bot changed the title feat: integral of f x • g y over α × β [Merged by Bors] - feat: integral of f x • g y over α × β Oct 12, 2023
@bors bors bot closed this Oct 12, 2023
@bors bors bot deleted the YK-integral-prod-smul branch October 12, 2023 17:47
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