chore: tidy various files

[Ruben-VandeVelde]

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[github-actions]

PR summary d23aee9c01

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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Decrease in tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type
502	-1	porting notes

Current commit 1e5996c79c
Reference commit d23aee9c01

You can run this locally as

./scripts/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).

[grunweg]

Thanks for this clean-up. Looks nice, as usual - just minor comments.
bors d+

[grunweg]

Suggested change

	`⨅ (x ∈ s) (y ∈ t), edist x y ≠ 0`. This is the property required for the Carathéodory's theorem
	`⨅ (x ∈ s) (y ∈ t), edist x y ≠ 0`. This is the property required for Carathéodory's theorem

[grunweg]

Suggested change

	/-- Carathéodory's theorem. If `m` is a metric outer measure, then every Borel measurable set `t` is
	/-- **Carathéodory's theorem**: If `m` is a metric outer measure, then every Borel measurable set `t` is

[grunweg]

optional

Suggested change

	(fun a _ => mem_setOf.mpr <|
	⟨hxi.pow a, fun φ => by simp [pow_le_one₀ (norm_nonneg (φ x)) <| hx φ]⟩)
	(fun a _ ↦ mem_setOf.mpr <|
	⟨hxi.pow a, fun φ ↦ by simp [pow_le_one₀ (norm_nonneg (φ x)) <| hx φ]⟩)

[grunweg]

I'll presume these proofs are not eyeball-slower?

[grunweg]

Ditto

[mathlib-bors]

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