feat(Analysis/SpecialFunctions/Log): log_prod for Multiset

[fbarroero]

We add

lemma log_prod' {α : Type*} {s : Multiset α} {f : α → ℝ} (hf : ∀ x ∈ s, f x ≠ 0) :
    log (s.map f).prod = (s.map (fun x ↦ log (f x))).sum

which generalizes

theorem log_prod {α : Type*} {s : Finset α} {f : α → ℝ} (hf : ∀ x ∈ s, f x ≠ 0) :
    log (∏ i ∈ s, f i) = ∑ i ∈ s, log (f i) 

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[github-actions]

PR summary d95168ed4d

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

+ log_prod'

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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No changes to technical debt.

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).

[riccardobrasca]

I am pretty sure the convention is that the bla_prod lemma refers to finsets (as here), and the multiset version is called something like bla_multiset_prod.

[eric-wieser]

Could you add the List version while you're at it? The multiset version should be provable in one or two lines in terms of it.

[eric-wieser]

Or should this be the simpler

Suggested change

	log (s.map f).prod = (s.map (fun x ↦ log (f x))).sum := by
	log s.prod = (s.map log).sum := by