feat(MeasureTheory): weaken hypotheses on the continuity-multiplication and xˢ·exp(-xᵖ) integrability lemmas

[dennj]

This is a generalization PR:

• IntervalIntegrable.{smul_continuousOn, continuousOn_smul} and the LocallyIntegrableOn analogues now need only IsBoundedSMul 𝕜 E instead of NormSMulClass 𝕜 E.
• integrableOn_rpow_mul_exp_neg_rpow / …_mul_rpow are generalized from 1 ≤ p to 0 < p (via u = xᵖ), matching the 0 < p of integral_rpow_mul_exp_neg_rpow.

Both follow from reproving these lemmas through the existing Integrable.bdd_mul/bdd_smul (since IntegrableOn f s μ = Integrable f (μ.restrict s)), which also makes the IntegrableOn.*_continuousOn(_of_subset) helpers redundant; they're removed.

[github-actions]

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[github-actions]

PR summary f930c8eda2

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

- IntegrableOn.continuousOn_mul
- IntegrableOn.continuousOn_mul_of_subset
- IntegrableOn.continuousOn_smul
- IntegrableOn.continuousOn_smul_of_subset
- IntegrableOn.mul_continuousOn
- IntegrableOn.mul_continuousOn_of_subset
- IntegrableOn.smul_continuousOn
- IntegrableOn.smul_continuousOn_of_subset

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit f930c8e).

• +0 new declarations
• −8 removed declarations

-MeasureTheory.IntegrableOn.continuousOn_mul
-MeasureTheory.IntegrableOn.continuousOn_mul_of_subset
-MeasureTheory.IntegrableOn.continuousOn_smul
-MeasureTheory.IntegrableOn.continuousOn_smul_of_subset
-MeasureTheory.IntegrableOn.mul_continuousOn
-MeasureTheory.IntegrableOn.mul_continuousOn_of_subset
-MeasureTheory.IntegrableOn.smul_continuousOn
-MeasureTheory.IntegrableOn.smul_continuousOn_of_subset

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit f930c8eda2
Reference commit bf69091c35

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[CoolRmal]

We already have MeasureTheory.Integrable.bdd_mul and MeasureTheory.Integrable.bdd_smul, and these lemmas can also be directly applied to IntegrableOn as IntegrableOn is just Integrable w.r.t a specific kind of measures. I don't want to discourage new contributors, but I don't see the point of your PR and I suggest you to close it.

[dennj]

We already have MeasureTheory.Integrable.bdd_mul and MeasureTheory.Integrable.bdd_smul, and these lemmas can also be directly applied to IntegrableOn as IntegrableOn is just Integrable w.r.t a specific kind of measures. I don't want to discourage new contributors, but I don't see the point of your PR and I suggest you to close it.

Ohh thanks, yes bdd_mul/bdd_smul were duplicated and I removed them.
However the PR contains real generalizations.