Talk:Elementary event

message: There seems to be another definition of elementary event. Suppose, there is an event E. If, for any event A from the sample space, ether A or "not A" must happen when E happens, then E is an elementary event. If this definition is correct then the article in its present form describes the concept of just an event rather than the elementary event.
The difference is actually quite important. Existence of elementary events is not guaranteed. For example, the Wigner function in quantum mechanics is the quasi-probability distribution over phase space points which, by themselves, are not elementary events (one can't measure coordinate and momentum simultaneously).  —Preceding unsigned comment added by 67.184.128.248 (talk) 07:30, 8 June 2009 (UTC)
thread_title:  Just an event? 

message: :"{HH}, {HT}, {TH} and {TT} if a coin is tossed twice. S = {HH, HT, TH, TT}. H stands for heads and T for tails."
All of {HH}, {HT}, {TH} and {TT} describe compound events.  An elementary event is, all over the web in disparate sources, defined as an event containing one element only.  Please correct me if I'm wrong.  — Preceding unsigned comment added by Scholarly (talk • contribs) 13:15, 30 December 2010 (UTC)
thread_title:  You gave an example of a compound event for an elementary event, didn't you? 

message: The example with heads and tails of a fair coin is the only example of elementary events which Kolmogorov himself gives in his "Foundations of the Theory of Probability". It appears that for him the concept of "elementary event" is basic and self-evident, comparable in spirit to the concept of a point in Euclidian geometry. The major purpose of elementary events in Kolmogorov's formulation of probability axioms is to introduce a set of objects on which one can postulate an integrable measure. However, it does appear that elementary events have some properties which are tacitly assumed: a) they are disjoint and b) an occurrence of a particular elementary event determines whether any other random event has occured.
Kolmogorov spends quite some time discussing the internal consistency and completeness of his system of axioms. Ironically, he does not discuss the realm of their applicability in the real world, although it is clear that there are phenomena (e.g., measurements of non-commuting variables in quantum mechanics) for which a space of "elementary events" can not be constructed.  —Preceding unsigned comment added by 129.118.29.133 (talk) 21:05, 25 January 2011 (UTC)
thread_title:  You are wrong... 

message: I would have thought in a probability space (\Omega, \mathcal{F}, P), you had \mathcal{F} as the σ-algebra of events, so an element of the sample space \omega \in \Omega does not have to be an event.  You do not have \omega \in \mathcal{F} and do not need to have \{\omega\} \in \mathcal{F} and, if not, then it would not be an elementary event.  Instead I would have thought an elementary event here would be a non-empty element of \mathcal{F} which did not have a non-empty proper subset. 2A00:23C6:148A:9B01:A549:DCEF:21E2:BF5C (talk) 02:46, 17 February 2024 (UTC)
thread_title:  Must an elementary event be an element of the sample space?