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@IshiguroYoshihiro IshiguroYoshihiro commented Nov 18, 2025

Motivation for this change

This PR define null_set and use this for definition of nu `<< mu.
following, e.g., https://proofwiki.org/wiki/Characterization_of_Null_Sets_of_Variation_of_Signed_Measure
(definition for signed measures)

The previous definition can be recovered using the lemma
measure_null_dominatesP for contents and the lemma charge_null_dominatesP
for signed measures (https://proofwiki.org/wiki/Category:Absolutely_Continuous_Signed_Measures)

We recover the definition of nlab
(a null B satisfied m(A | B) = m(A), https://ncatlab.org/nlab/show/null+subset
or https://www.math.uwaterloo.ca/~beforres/PMath451/Course_Notes/Chapter4.pdf
Def 2.2.2) as the lemma null_setU.

fixes #1754

Checklist
  • added corresponding entries in CHANGELOG_UNRELEASED.md
  • added corresponding documentation in the headers

Reference: How to document

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@affeldt-aist affeldt-aist added the enhancement ✨ This issue/PR is about adding new features enhancing the library label Nov 18, 2025
@affeldt-aist affeldt-aist added this to the 1.15.0 milestone Nov 18, 2025
@affeldt-aist affeldt-aist marked this pull request as ready for review November 18, 2025 06:04
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@holgerthies

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https://proofwiki.org/wiki/Characterization_of_Null_Sets_of_Variation_of_Signed_Measure This lemma should be useful too.

Maybe turn this comment into a "wish" issue.

@affeldt-aist affeldt-aist force-pushed the proper_measure_dominates_20251111 branch from fcd460e to b1d4353 Compare November 24, 2025 12:43
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@holgerthies

ping :-)

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rename induced -> induced_charge

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