# Certain event

From Encyclopedia of Mathematics

An event which is known a priori to be certain to occur. More exactly, if $ \Omega = \{ \omega \} $
is the space of elementary results, an event $ A $
which occurs together with any of the elementary results $ \omega $
is said to be certain, and must clearly coincide with the entire space $ \Omega $.
It is then natural to ascribe the probability 1 to a certain event:

$$ {\mathsf P} ( A) = \textrm{ measure } \{ \omega : {\omega \in A } \} = {\mathsf P} ( \Omega ) = 1 . $$

An impossible event is an event complementary to $ A $.

**How to Cite This Entry:**

Certain event.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Certain_event&oldid=46300

This article was adapted from an original article by A.V. Prokhorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article