Fill the finitely additive measure calculus in Exercise 1.4.20 - #718
Open
Chessing234 wants to merge 6 commits into
Open
Fill the finitely additive measure calculus in Exercise 1.4.20#718Chessing234 wants to merge 6 commits into
Chessing234 wants to merge 6 commits into
Conversation
…e, and finite unions. These are the set operations used in the finitely additive calculus.
A measurable subset splits off a nonnegative remainder, so its measure cannot exceed the larger set.
Disjoint finite unions reduce to binary additivity by induction on the index set.
The union is at most the sum of the pieces after splitting off a disjoint remainder.
… measures. Both sides split along the disjoint remainder F \\ E.
Additivity on EReal is left-biased, so the comparison has to add the same first summand on both sides.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
1 participant
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Summary
Test plan
lake build Analysis.MeasureTheory.Section_1_4_3; CI covers the module.Made with Cursor