" ... a sample space
(which will be a probability space)"
is, in a word, wrong. The sample space will be part of a probability space but will not "be a probability space".
is, in a word, wrong. The sample space will be part of a probability space but will not "be a probability space".
Some intuitive overviews, clearly labeled as such, are fine and can be helpful, but "idiomatic language" just is not. Won't find such in the writings of W. Rudin, P. Halmos, J. Neveu, or any of a long list of authors of some of the best math books. In a good math or computer science journal, a reviewer or the editor would likely reject "idiomatic language".
The definitions I gave are the accepted ones.