No, it’s not only the statement that the probability of an event is a set. The definition of the probability that follows this statement, and many other, are confusing.

Since I received messages in my julia discourse inbox, asking why I manifest such an attitude,

and the author friends appreciated the arguments given by @rikh, I give here my arguments and the right Kolmogorov axioms, not in a PR or an issue opened on the book repo.

I stumbled upon a link to juliadatascience.io here on discourse. The first click was on the section Distribution. I didn’t know it is a work in progress. But even for a WIP the presentation must be clear, and correct, if it is already posted online, because it can be read by a lot of people. That’s why I posted that message on discourse.

I give here a link to a pdf, I edited as an answer: https://drive.google.com/file/d/1dOgOWk3kUKnYnpkuxMH2JAvR1AP7TuCJ/view?usp=sharing

If you have read the text in the above pdf file you can now compare with author axioms.

The image below illustrates how incorrect is their “axiom” stating that for any two mutually exclusive events, A, B, `P(A)=1-P(B)`

.

Involving a probability density function in the definition of the probability (their third axiom) is totally unacceptable, because at that point we don’t know completely what a probability is, and much less a probability density. It’s a logical error.

As I said the list of unacceptable definitions in the section Distributions is much longer, but I consider that the authors must clarifies first, for themselves, all involved notions and present them in their own words.