View source for Certain event

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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|impossible event]] is an event complementary to  $  A $.