List of sample space perspectives: Difference between revisions

Latest revision as of 14:52, 15 January 2019

In probability theory, one can take several perspectives of what the sample space (often denoted $\Omega$ ) means. We record several of these here.

Possible worlds and possible world histories [1]
Sources of randomness, and extending the sample space [2] [3]
"One often analyses such situations by jumping to the final extension of the sample space after the game has completely played out, viewing times prior to the final time as being associated to various sub-sigma-algebras of the final sigma algebra, but one can also take a more “real-time” perspective, thinking of the sample space as dynamically evolving over time. The choice of which perspective to use is to some extent a matter of personal taste." [4]

@@ Line 3: / Line 3: @@
 * Possible worlds and possible world histories [https://www.greaterwrong.com/posts/JdK3kr4ug9kJvKzGy/probability-space-and-aumann-agreement]
 * Sources of randomness, and extending the sample space [https://terrytao.wordpress.com/2010/01/01/254a-notes-0-a-review-of-probability-theory/] [https://terrytao.wordpress.com/2015/09/29/275a-notes-0-foundations-of-probability-theory/]
+* "One often analyses such situations by jumping to the final extension of the sample space after the game has completely played out, viewing times prior to the final time as being associated to various sub-sigma-algebras of the final sigma algebra, but one can also take a more “real-time” perspective, thinking of the sample space as dynamically evolving over time. The choice of which perspective to use is to some extent a matter of personal taste." [https://terrytao.wordpress.com/2015/09/29/275a-notes-0-foundations-of-probability-theory/#comment-460159]
+==See also==
+* [[Disappearance of sample space]]
 [[Category:Probability]]