**standard measurable space of 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 $\mathbb{N}$ |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Boolean algebra

▾ Sigma-algebra

▾ Discrete sigma-algebra

▾ Discrete measurable space

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Subset

▾ Power set

▾ Hyperpower set sequence

▾ Hyperpower set

▾ Hypersubset

▾ Subset algebra

▾ Boolean algebra

▾ Sigma-algebra

▾ Discrete sigma-algebra

▾ Discrete measurable space

Formulation 1

An D548: Ordered pair $M = (\mathbb{N}, \mathcal{P}(\mathbb{N}))$ is the **standard measurable space of 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 $\mathbb{N}$ |