[Merged by Bors] - feat: strong law of large numbers for vector-valued random variables #7218
Conversation
This file contains 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
sgouezel
added
awaiting-review
t-measure-probability
eric-wieser
reviewed
Sep 17, 2023
eric-wieser
reviewed
Sep 17, 2023
RemyDegenne
added
awaiting-author
Co-authored-by: Rémy Degenne <remydegenne@gmail.com>
sgouezel
added
awaiting-review
and removed
awaiting-author
|
bors r+ |
bors bot
pushed a commit
that referenced
this pull request
Sep 26, 2023
…7218) We already have the strong law of large numbers for real-valued integrable random variables. We generalize it to general vector-valued integrable random variables. This does not require any second-countability assumptions as integrable functions can by definition be approximated by simple functions, for which the result is deduced from the one-dimensional one. Along the way, we extend a few lemmas in the library from the real case to the vector case, and remove unneeded second-countability assumptions.
|
Pull request successfully merged into master. Build succeeded! The publicly hosted instance of bors-ng is deprecated and will go away soon. If you want to self-host your own instance, instructions are here. If you want to switch to GitHub's built-in merge queue, visit their help page. |
bors
bot
changed the title
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
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Outdated suggestions cannot be applied.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.
We already have the strong law of large numbers for real-valued integrable random variables. We generalize it to general vector-valued integrable random variables. This does not require any second-countability assumptions as integrable functions can by definition be approximated by simple functions, for which the result is deduced from the one-dimensional one.
Along the way, we extend a few lemmas in the library from the real case to the vector case, and remove unneeded second-countability assumptions.