We have seen that the event and are equivalent and .The underlying sample space is omitted in notation and we simply write and instead of and respectively.
Consider the Borel set , where represents any real number. The equivalent event is denoted as .The event can be taken as a representative event in studying the probability description of a random variable . Any other event can be represented in terms of this event.
For example,
and 
are equivalent and 
.The underlying sample space is omitted in notation and we simply write 
and 
instead of 
and 
respectively. 
, where 
represents any real number. The equivalent event 
is denoted as 
.The event 
. Any other event can be represented in terms of this event.
For example,