Elementary event

Elementary event, basic event, atomic event, element of a probability space or result is called an element of the result set in a probability space.

Basics

The probability space is then the totality of

• The result set (also basic room )
• The elementary events or results
• A system of subsets ( events ) of, the algebra of events
• And the probability measure.

It should be noted that a natural event, despite its name is not an event of a probability space. An event is defined as a member of the event algebra, and thus no element but a portion of the base region. Although one can identify the elements of the base space with its singleton subsets, but these are one-element subsets only in the event algebra if this represents the power set of the base space.

In the important special case of discrete probability spaces ( with them is finite or countable infinite) is the power set of a suitable algebra of events. In this case, in particular all identifiable with the elementary events singleton subsets in the algebra of events are included, ie the elementary events are actually also events of the probability space.

Term

The term " act of God " for the elements of the probability space goes back to Kolmogorov himself, although this difference also between the elements of the result set and its singleton subsets, introduced but not have their own name for the latter. Recent literature used in contrast rather the names " result" or " output " and " event" is clearly understood as a set consisting of results. In addition, then, in the case of discrete probability spaces " elementary event " instead to denote the singleton events (ie, for subsets) used.