A marked point process in the simple temporal setting with mark space 
is a double sequence
 |
of 
-valued
random variables 
and 
-valued random variables 
defined on a probability
space 
such that 
is a simple
point process (SPP) and:
1. 
for 
;
2. 
for 
.
Here, ![R^^^+=(0,infty]](/images/equations/MarkedPointProcess/Inline12.svg)
,
denotes probability, and 
denotes the so-called irrelevant mark, chosen outside 
and used for an event that never occurs.
The extended mark space is 
.
This definition is similar to the definition of an SPP in that it describes a sequence of time points marking
the occurrence of events. The difference is that these events may be of different
types where the type (i.e., the mark) of the 
th event is denoted by 
. Note that, because of the inclusion of the irrelevant mark
,
marking will assign values 
for all 
--even when 
, i.e., when the 
th event never occurs (Jacobsen 2006).
