**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 $M$ |