A triple $M = (\mathbb{N}, \mathcal{P}(\mathbb{N}), \#)$ is the standard counting measure space of basic natural numbers if and only if

(1)	$\mathbb{N}$ is the D225: Set of natural numbers
(2)	$\mathcal{P}(\mathbb{N})$ is a D80: Power set for $\mathbb{N}$
(3)	$\#$ is the D5637: Standard basic natural number counting measure on $M$