A simple point process (or SPP) on the positive time axis, with almost surely finitely many events in every bounded time
interval, can be represented by an almost
surely increasing sequence of strictly
positive, possibly infinite random
variables which are strictly increasing
as long as they are finite and whose almost sure limit is 
. Symbolically, then, such an SPP is a sequence 
of 
-valued random variables
defined on a probability space 
such that
1. 
,
2. 
,
3. 
.
Here, ![R^^_0=[0,infty]](/images/equations/SimplePointProcess/Inline8.svg)
and for each 
,
can be interpreted as either the time point at which the
th
recording of an event takes place or as an indication that fewer than 
events occurred altogether if 
or if 
, respectively (Jacobsen 2006, pp. 9-10).
