Can the range of a variable be inclusive infinity? Can a range be $[0, \infty]$ or must it be $[0, \infty)$ because you can never quite reach infinity?
Clarification: 
$[0, 1]$ means $0 \leqslant x \leqslant 1 $, while  $(0, 1)$ means $0 < x < 1 $. My question is whether infinity can be written as inclusive when stating the range.


An example of where this is actually used are measure functions. For instance, the Lebesgue measure, $\lambda$ on (certain subsets of) $\Bbb R$ has the property that $$\lambda((a,b)) =  b-a $$
when $a,b$ are finite, while, for example $$\lambda(\Bbb R) = \infty$$.
