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define null set and fix the definition of domination of measure/charge #1760
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define null set and fix the definition of domination of measure/charge #1760
IshiguroYoshihiro
wants to merge
10
commits into
math-comp:master
from
IshiguroYoshihiro:proper_measure_dominates_20251111
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https://proofwiki.org/wiki/Characterization_of_Null_Sets_of_Variation_of_Signed_Measure |
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Maybe turn this comment into a "wish" issue. |
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ping :-) |
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Motivation for this change
This PR define
null_setand use this for definition ofnu `<< 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_dominatesPfor contents and the lemmacharge_null_dominatesPfor 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
CHANGELOG_UNRELEASED.mdReference: How to document
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