According to [this](https://www.statlect.com/fundamentals-of-probability/legitimate-probability-mass-function) and [this](https://www.statlect.com/fundamentals-of-probability/legitimate-probability-density-functions), we can say that a function f is pmf/pdf **iff** f is non-negative and the sum/integral over... is 1.

But for example, for pmf, there is also a property called "[countable additivity](https://en.wikipedia.org/wiki/Sigma_additivity)". Do we also have to check this property?