[Merged by Bors] - feat(MeasureTheory): add MeasurableEmbedding.natCast

[huaizhangchu]

This PR adds a lemma stating that the coercion from ℕ is a measurable embedding.

This is useful for proving properties about discrete probability distributions on ℕ by lifting them to ℝ and will be used in #34435.

[github-actions]

PR summary e8ea1afc32

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

+ natCast

You can run this locally as follows

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

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

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

---

No changes to technical debt.

You can run this locally as

./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).

[huaizhangchu]

-awaiting-author

[RemyDegenne]

Thanks!
bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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