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The Radon-Nikodym derivative of the pushforward of two measures is written as a conditional expectation.
This will be useful to prove the data processing inequality for the Kullback-Leibler divergence (or more generally f-divergences).


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@RemyDegenne RemyDegenne added the t-measure-probability Measure theory / Probability theory label Feb 10, 2026
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github-actions bot commented Feb 10, 2026

PR summary 2cfa21a49b

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.MeasureTheory.Function.ConditionalExpectation.RadonNikodym (new file) 2383

Declarations diff

+ SigmaFinite.of_trim
+ rnDeriv_trim
+ toReal_rnDeriv_map
+ toReal_rnDeriv_map_ae_eq_trim
+ toReal_rnDeriv_trim

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.


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).

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