Editing Elementary event (section)

==Probability of an elementary event==

Elementary events may occur with probabilities that are between zero and one (inclusively). In a [[Discrete random variable|discrete]] probability distribution whose sample space is finite, each elementary event is assigned a particular probability. In contrast, in a [[Continuous random variable|continuous]] distribution, individual elementary events must all have a probability of zero.

Some "mixed" distributions contain both stretches of continuous elementary events and some discrete elementary events; the discrete elementary events in such distributions can be called '''atoms''' or '''atomic events''' and can have non-zero probabilities.<ref>{{cite book|last=Kallenberg|first=Olav|title=Foundations of Modern Probability|edition=2nd|year=2002|page=9|url=https://books.google.com/books?id=L6fhXh13OyMC|publisher=Springer|location=New York|isbn=0-387-94957-7}}</ref>

Under the [[Measure theory|measure-theoretic]] definition of a [[probability space]], the probability of an elementary event need not even be defined. In particular, the set of events on which probability is defined may be some [[Sigma-algebra|σ-algebra]] on <math>S</math> and not necessarily the full [[power set]].