Actually it is, since measure theory and the Kolmogorov construction of probability is only one way to build an axiomatic theory of probability. It just happens

Actually it is, since measure theory and the Kolmogorov construction of probability is only one way to build an axiomatic theory of probability. It just happens to be the one most of us learn first. Its a bit like asking if the set of all sets that do not contain themselves is contained in itself. The question makes no sense in set theory, but it leads to important extensions. Edit: Have a look at the Borel–Kolmogorov paradox, and approaches to consolidate it https://link.springer.com/article/10.1007/s11229-016-1070-8 https://link.springer.com/article/10.1007/s11229-016-1070-8